In Invictus, Morgan Freeman makes an attempt to sound like someone from South Africa but slips back into his natural accent halfway through each line.
In August Rush the English actor Freddie Highmore plays an American boy who's lived just outside New York all his life. Granted it was the first time Freddie had to put on an American accent, but it was weak and often slipped.
In The Town the English actress Rebecca Hall plays American bank manager Claire Keesey. Her accent subtlely slips throughout the movie, one example being in the scene where her character and Doug (Ben Affleck) are on a date and run into Jem (Jeremy Renner). The line "So I've been telling all my friends about you," is clearly said in a British accent.
In The Third Man, Alida Valli (playing Anna) obviously believed that it it would be appropriate to use several English accents in her role as an east-European escapee of Communism; One time it's Russian, another time it's perfect British English, then it's German English, then one time it's American English, then Dutch English.
In Stardust, Michelle Pfeiffer plays an English witch with English sisters, who have actual English accents. Pfeiffer attempts an English accent, which works now and then in the film, but often sounds horrendous.
In Pacific Rim, Charlie Hunnam's American accent varies between "poorly attempted" and "nonexistent." His overpronunciation of the rhotic 'r' characteristic to American English is painfully conspicuous.
In the film Michael Collins, most of the cast are Irish and have according accents. The female lead is Julia Roberts, whose accent slips from Irish to Southern twang every time she's on screen, most jarringly in her first scene.
The eponymous male lead was played quite well by Irish actor Liam Neeson, but not with the appropriate Cork accent.
For more bizarre vocalizing from Julia Roberts, see her performance as Irish maid Mary Reilly in the film of the same name.
In Big Game, British Jim Broadbent and Ray Stevenson portray American Morris and Herbert, but in both cases, you can hear their native accent from time to time.
The King of Accent Slippage is Sean Bean. His native South Yorkshire accent escapes in virtually all of his movies — including GoldenEye where he refers to James in a way that wouldn't be out of place in Emmerdale. Count Vronski in Anna Karenina wasn't from Sheffield.
Liam Neeson, usually when he has to say anything with an "oo" sound, like "you". He's become better at it as he's gotten older, but some of his early films like Darkman are a fairly egregious case of this trope.
Brit Claire Forlani plays Brandi Svenning in Mallrats, set in New Jersey. Her accent is decidely unJoisey and her natural English accents slips in quite often. It's especially noticeable in the opening scene, filmed long after the original production wrapped and absolutely no one was happy to be there, according director Kevin Smith.
In The Dark KnightGary Oldman's accent slips throughout the movie but is especially evident during the scene on the roof when he, Harvey Dent, and Batman are discussing what to do about Lau.
Played with in Nim's Island, in which Gerard Butler plays Alex Rover, with his natural accent, as well as Nim's father, with a Fake American accent that is truly embarrassing to hear, even when the Scottish vowels and Rs aren't forcing their way out.
Best seen in the scene where Nim and her father are reunited. About a minute of relieved, Scottish-accented ranting, then he switches back to American in the space of a glance.
Really, Butler could be the Trope Codifier. Just about every film has his accent come out at some point. Notably, the trailer for The Bounty Hunter has him utter the line "duly noted" in a manner where one can slightly detect it.
Happens in Raiders of the Lost Ark too. Listen to both Paul Freeman (Belloq) and John Rhys-Davies (Sallah). Both their British accents shine through during the dig scenes.
Keanu Reeves gave a not great English accent (with few passable moments) for the first half of or so of Bram Stoker's Dracula, but by the end of it the poor fellow seems to have forgotten that Jonathan Harker was not raised in Canada (he was born in Beirut, Lebanon and raised in Toronto).
Same goes for The Devil's Advocate: he seemingly arbitrarily alternates between his natural accent and a Southern-sounding accent (the latter being more appropriate for his character). As with Bram Stoker's Dracula, he basically abandons the second accent about halfway through.
In general, Ray Milland has a hard time hiding his Welsh accent. Specifically in Easy Living, his American accent comes and goes, mixing into a strange hybrid at times.
In the Australian slasher film Nightmares from 1980, the central character's accent swings back and forth wildly between something resembling an Australian accent and something resembling an American accent. She was an American trying to sound Aussie, but her accent lapsed so regularly that it really was a 50/50 chance guessing which was the real one.
Richard Gere is apparently supposed to be an ex-IRA man (i.e. most likely from Norn Iron) in The Jackal. Don't know what accent he was going for though.
Also, Richard Gere's poor excuse of a British accent in First Knight.
In the Conan the Barbarian (1982) film, surfing champion Gerry Lopez played Subotai the Hyrkanian with a vaguely foreign accent (the Hyrkanians were effectively proto-Mongols), but occasionally slips into a California accent.
Though not a fictional role, per se, in Christian Bale's Epic Terminator 4 Rant, his normally convincing American accent slips generally in a direct relationship to his frustration and rage.
Although Bale's accent is his own bizarre Transatlantic creation nowadays. His Welsh birthplace is often mentioned but he has never sounded remotely Welsh - probably because his English family only lived there temporarily. His natural voice (seen in his earliest movies like Empire of the Sun) is RP Southern English.
In the actual film, Sam Worthington's American is extremely shaky (it still wobbles a bit in Avatar, but he has improved). Worthington reverts to his own accent for several minutes in the middle of the film, when he's in bondage and having a heart-to-heart with Bale, making one wonder how it was able to slip past the cast, the director, the crew, the editors, and the test audience.
His American accent in American Psycho, while at times jarring, actually works there, with its imperfections actually helping to subtly enhance the nature of Patrick Bateman's character. While the dialect is usually spot-on, it comes off as obviously put on, as if Batemen was trying way too hard to sound normal. One noticeable slip does occur though in the limo scene near the beginning of the film, with his mangled pronunciation of the name Palmer.
Bale's accent slips a few times in The Machinist, especially when he's angry, but in other places too. Check out the scene at the DMV, particularly the line "I wouldn't ask if it weren't extremely important."
In The Dark Knight, in the scene where Bruce Wayne crashes into the police escort, Bale's accent slips away.
In Public Enemies, Bale's portrayal of BOI Agent Melvin Purvis has him attempting a southern drawl every other scene.
The 39 Steps has Robert Donat playing a Canadian vacationing in London. Somewhere around the final act, he slips more and more into his British accent.
In the Street Fighter movie, although Jean-Claude Van Damme maintains a pretty good American accent, during the speech towards the end, when he announces that he'll "kick that son of a bitch Bison's ass", try not to hear his native Belgian accent. The rest of the movie probably qualifies as well. "If Sagat runs (unintelligible) to Bison..."
Of the same movie, some critics have complained that Sean Astin's accent as Samwise sounds slightly Cockney. This may be because before shooting started, Astin — realizing that there were upper- and lower-class accents in England, but failing to realize there were urban and rural accents — rehearsed the role on his own with a Cockney accent.
He does slip just once, though - in Rivendell, when he says, "We did what Gandalf wanted, didn't we?" The 'wanted' comes out sounding American.
Less evident than the above, but there were a couple of times when Elijah Wood's accent seemed to be wavering, though it is mostly good.
Notably averted by Brad Dourif, whose pronounced West Virginia drawl never makes an appearance.
Caroline Rhea in The Perfect Man is supposed to be from Brooklyn. The accent comes and goes. Mostly, it goes.
Alec Baldwin's Southern accent occasionally disappears completely in Ghosts of Mississippi.
In The Insider, the British Michael Gambon has one scene as Brown & Williamson CEO Thomas Sandefur in the Louisville, Kentucky scenes. His accent goes back and forth between the South and England.
Admittedly, only once, with Gambon's delivery of the line "It's spooky how he can concentrate!". Otherwise, he sounds very much southern just like the real Thomas Sandefur was.
In the film Mary Poppins, Dick Van Dyke puts on a painful cockney accent that comes and goes depending on what scene he's in.
In Blood Diamond, Leonardo DiCaprio does a passable Rhodesian accent until one scene in which he shouts at Djimon Honsou for going another way. As he raises his voice, he reverts back into his normal American accent.
Kate Beckinsale as Anna Valarious in Van Helsing is unable to maintain an Eastern European accent for longer than a couple of lines at a time. She eventually gives up completely about halfway through the movie. To their credit, the Brides of Dracula didn't even try to sound anything other than American (even though only one of the three brides is actually American).
In Volunteers, Tom Hanks' bad New English "Haahvahd" accent flips on and off like a lightning bug.
He uses a similar one in Catch Me If You Can. It's improved a lot in 20 years, but still wobbles a little on occasion.
In the outtakes, he attempts to say a line through a mouthful of food ("She thinks he's Connors") and then asks "but could you hear the accent?"
In Forrest Gump, the way he yells "Greenbow, ALABAMA!" is much more Tom Hanks' voice than Forrest Gump's.
Basil Rathbone's French accent in Captain Blood sometimes gives way to his native British South African in the middle of sentences.
Clive Owen's American accent for Derailed slips for just a teensy line near the end where he pops in the hotel room to tell a stranger he's being scammed. The word "scam" comes out in his original British accent.
Additionally, he seems to attempt an American accent for about half of the first scene in Inside Man. Drops it pretty quickly after that, and it never resurfaces.
Eddie Izzard does this and then, upon realizing it, often hangs a huge lampshade on it. As here, in the same show, Definite Article:
Eddie(as Welsh Pavlov): Excellent. Changed my name from "Evans" to "Pavlov". Now "Gareth Pavlov" and fitting in well.
Eddie (during a James Bond scene): I am a Schmuf agent, and Ah have a voice synthesahzer in mah threut. Ah can do eny accent yu can theenk uv. Unfortunitly I've lowst the enstructions at the moment, and it's stuck on "shop deymonstraation."
Of course, he also uses "stock accents", such as parodying James Mason's accent for God in multiple shows and using Sean Connery for, among others, Henry VIII and Noah.
To bring two examples together, Eddie does an absolutely hilarious skewering of Dick Van Dyke's Cockney-by-way-of-Australia accent in his special Glorious
Done intentionally (and cleverly) in the film version of Watchmen. Adrian Veidt/Ozymandias, played by Matthew Goode, only speaks with a German accent when in the presence of people he's familiar with- presumably, because he's trying to sound "more American" to the general public.
This actually came about because the decision to play up Veidt's German background wasn't made until after the first scene in which he addresses the press - for which Goode used a generic American accent — had already been shot. Nevertheless, the end result is very effective, arguably more so than if Goode had simply spoken with a German twang throughout.
Goode also occasionally slips back into his native British, giving Ozymandias a grand total three different accents.
The Sci-Fi original movie Rock Monster has a supposedly Scandinavian character, who occasionally attempts a generic Eastern European accent.
According to some fans, this happens in Newsies to a humorous extent.
Christian Bale's Jack, in particular, sounds like he couldn't decide what New York accent to do and decided on all of them.
In Hannibal, Julianne Moore has Clarice's accent for her first few scenes and then drops it for the rest of the movie. Of course, Silence of the Lambs did establish Jodie Foster's Clarice was trying to lose her Southern accent, but who knew she'd accomplish it so suddenly?
It's quite glaring in certain scenes.
"Yew swear tew!"
There's a scene in Madhouse where temperamental horror icon Paul Toombes (Vincent Price) has just been disrespectful of his female costar's alleged unprofessionalism. She draws herself up to her full height and tells him exactly what she thinks. And then...
Toombes: Your stage accent is slipping.
In the X-Men movies, Australian Hugh Jackman didn't seem to experience accent slippage portraying the Canadian Wolverine, aside from an odd-sounding vowel here and there (glaring example: near the end of X2: X-Men United when he says "you don't wanna go that way, trust me"). These seem pretty well impossible to excise from Australian actors (compare to Cate Blanchett, Russell Crowe, Heath Ledger, etc., especially on O sounds).
Jackman slips into Australian in the first movie the first time he says, "Storm" (just before "What do they call you? 'Wheels'?"). And also in the truck, right after Rogue tells him that he should buckle up. And again when he says to Jean "Couldn't wait to get my shirt off again, could you?". And in the second movie, on the word "art" when talking to Bobby's parents.
His accent slip is most evident in the (in)famous line from Origins: "I know who you are Geeymbit!"
In the first film, Anna Paquin at least attempted to remember to give Rogue a southern accent on occasion. Seems like she gave up by the end of the third film, though.
Also in the first film, Halle Berry speaks, very briefly, in a vaguely foreign accent. This is made even more evident if you watch some of the deleted scenes. She completely abandons this by the end of the film. She may have been angling for a Sub-Saharan African accent, what with Storm being from Kenya in the comics. But it's worth noting even director Bryan Singer referred to it as an "attempt" in his DVD commentary.
As in the previous film, James McAvoy loses his English accent in favor of his native Scottish one when he shouts, "I don't want YA FUTCHA!" It's even more apparent when he's yelling at Erik on the plane because it comes out as, "YA ABONDONED MEH!"
Interestingly, it's averted with Michael Fassbender who maintains an Ian McKellen-esque English accent rather than slipping into his own Irish one as he did repeatedly in First Class.
The English Nicholas Hoult's American accent is pretty good, but he frequently messes up on the word "professor."
Hugh Jackman's Australian accent slips out in Wolverine's very first line of dialogue.
In Spider-Man 2, Alfred Molina, who plays Dr. Octopus, is from London. When he says, "I should've known Osborn wouldn't have the spine to finish you!," his British accent is audible.
He also has an epic one in Chocolat when he is talking to Father Henri doing his gardening. Molina forgets he is meant to French for the entire scene and speaks in his natural London accent.
In Thirteen Days, which is set during the Cuban Missile Crisis, Kevin Costner's Boston accent (he plays Kenny O'Donnell, a presidential aide to John F. Kennedy) is particularly atrocious. The other actors do better, but he horribly stretches out his vowels and just generally exaggerates everything in a really distracting way. It's especially noticeable considering that his character has a lot of the more dramatic dialogue, the other accented characters speaking a lot of stuff that is more-or-less lifted straight from transcripts of White House recordings.
Speaking of Kevin Costner, his portrayal of Robin Hood in Robin Hood: Prince of Thieves had a bare minimum of an accent. Apparently the accent he tried for the part was so horrendous that the director told him to speak normally.
He got much better at it in the sequels, but in the first film he slips, drops it for whole sentences, or (as the guys at RiffTrax point out) morphs into Christopher Walken.
In 21, English actor Jim Sturgess does what could charitably be called a decent American accent. Mostly. When he remembers.
In Goal!, Anna Friel, playing the Newcastle United club physician, does what could charitably be called a decent Geordie accent. Mostly. When she remembers.
The actors of The Shipping News attempted the Newfoundland accent with varying degrees of success. Extremely distracting, however, was American actress Julianne Moore's version of it, which usually settled on sounding like a badly-faked Irish accent.
Brendan Gleeson's American accent in Green Zone seemed to slip into Irish on the odd word which oddly enough made him sound somewhat Chicagoan.
About twenty minutes into the firstStar Wars movie, Princess Leia inexplicably gains a clipped, pseudo-British accent when dealing with her Imperial captors. It disappears after she is rescued and never returns again. (One could, if feeling charitable, chalk this up to her attempting to sound high-class, as the Coruscanti accent is close to British. Or possibly to mocking Admiral Tarkin's accent.)
Carrie Fisher, the actress, has explained this disappearing accent. The scene in question was the first scene she filmed, and because she was a Princess, she decided to put on the faux-British accent you hear. However, after filming finished, she and the filmmakers concluded it didn't sound right and dropped it in future scenes. Due to the film's tight budget and schedule, reshooting the scene without the accent was out of the question.
A later explanation Fisher gives during her one-woman show Wishful Drinking was that the accent was an after-effect of 18 months of studying at London's Central School of Speech and Drama where by necessity she picked up a Received Pronunciation accent.
In The Empire Strikes Back, the snowspeeder co-pilot Dack slips into a British accent when he says "Feeling alright, sir?" to Luke.
Natalie Portman in V for Vendetta. The character, Evey Hammond, lives in London. Portman's accent in the movie varies between Cockney, Australian, RP English and a strained-sounding American. Strangely, it comes across as quite endearing.
Occasionally in On Her Majesty's Secret Service you can hear George Lazenby (as James Bond) slip back into his native Australian accent. It's not especially noticeable as the 1960s Australian accent was a little more English-sounding anyway, but it's there.
In Doom, Karl Urban holds up his American accent awfully well. But as the film goes on, it gets shaky, especially when his character starts to yell.
Practically the entire cast of Doom, all of whom are supposed to be Americans, are British. This may be down to the fact that it was shot in eastern Europe and work permits are easier to get for EU locals. Even Richard Brake, playing Portman, was actually born in the UK (in Wales), though to all intents and purposes he's American. The only American-born American in the entire cast is Dwayne "The Rock" Johnson. Rosamund Pike is famously English, as are Deobia Oparei (Destroyer), Ben Daniels (Goat), Raz Adoti (Duke), Al Weaver (The Kid), and Yao Chin (Mac - going by the family name Takahashi, his character is supposed to be of Japanese descent, but somehow has three names, which is unknown in Japan). Dexter Fletcher is also in it with a risible attempt at American, but the others seem to do pretty well.
What's up with Sean Connery's accent in Marnie? It starts off as some sort of vaguely American thing before rolling back up the high country for an egg wrapped in sausage meat.
In The A-Team, Sharlto Copley uses a vaguely Southern accent which he has a hard time keeping up when he's excited (see the line "You gorgeous old rust bucket, you! Did you miss your daddy?", which is entirely in his natural South African accent) or shouting. Though it kind of works for the character.
Though given that it's Murdock, it's entirely possible a lot of it was intentional, particularly the 'gorgeous old rust bucket' and 'heat seekers' lines.
In fact, it's probably all intentional, given that in the original TV show, Murdock uses no less than five different accents in the pilot episode alone.
It's used deliberately in a brief scene where he impersonates a South African reporter.
Mel Gibson in Braveheart. ([Gibson's American accent] "We won at Stirling!" [Scottish accent] "And still you quibble!")
Gibson had a hard time ditching his Australian accent earlier in his career. The first two Lethal Weapon movies have lots of little bits and pieces of it peppered in. The "gold pen" speech in Lethal Weapon 2 stands out in particular.
Brit Aaron Johnson does a decent job with an American accent in Kick-Ass, although towards the end he mentions being troubled by the "idear" of never seeing his friends and family again when he thinks he's about to be killed.
In L.A. Confidential, it seems more like James Cromwell is occasionally slipping out of his native American accent. He plays the Irish-American Capt. Dudley Smith in the movie, but most of the time he sounds American, occasionally with a terrible Irish accent. It's most notable when he says Irish things like "boyo."
'Boyo', of course, being a stereotypically Welsh thing to say.
In the novel, it's made a bit more clear that Dudley Smith takes care to cultivate the stereotypical Irish Cop image, so that people will underestimate him, in a sort of native variety of Funny Foreigner.
Kate Winslet managed a pretty decent American accent in Titanic (1997), but it did falter in a couple places. Watch the sequence where she tells Jack that she is engaged.
Considering she is returning from England, it could be argued that her character may have picked up an affected accent on the trip.
Winslet does far better when she plays the role of Clementine in Eternal Sunshine of the Spotless Mind. There are a handful of small mistakes, but they're not noticeable unless you're deliberately paying attention to her pronunciation.
In National Treasure, Diane Kruger's attempts at a nondescript American accent fall short quite often under scrutiny. The accent-masking is convincing when it isn't slipping, but the slips are very noticeable.
Cary Elwes's agent (or manager, or somebody) apparently convinced him a few years ago that he should lose his native accent - he mentioned this on The Tonight Show or somesuch once. This falls somewhere below Ishtar, but not too far below, in Disasters which might have been avoided.
Brad Pitt is something of a serial offender in this field, most notably in The Devil's Own where he plays an IRA bomber hiding out in New York: he's full-on "terty-tree-and-a-turd" Oirish for the most part, despite his character being from Northern Ireland, but starts to lose it when the waterworks get going for the climax.
It appears he's not even trying in 12 Years a Slave. For a "Canadian" he sounds awfully Southern.
A Man Of No Importance: for whatever reason, Albert Fiiney is flat-out incapable of pronouncing the "R" sound. Ths makes it a little harder to enjoy his portrayl a an Irish theatre director trying to organise rehoouusals.
Marlon Brando in The Missouri Breaks. He starts off with an exaggerated ''top o' the mornin' " Irish accent, which is quite jarring since the film's set in the Old West and his character's named Robert E. Lee Clayton. But later in the film this accent's gone and Brando's back to his natural voice. Supposedly Brando claimed that this was deliberate, to show that Clayton was mentally ill.
Burt Lancaster, an American, portrayed Irish born Colonel Anthony Durnford in the film Zulu Dawn. Lancaster's Irish accent slips in and out several times. It doesn't help matters that he's the only American in the cast surrounded by big name British actors, including Irish born Peter O'Toole.
Jim Carrey in any of his earlier movies. While his characters are not outright stated to be American, one assumes anyway. Certain words are very glaring to his Canadian accent (e.g., "borrow," "progress"). To be fair, he either doesn't try to hide it or doesn't think to do so.
According to some accounts, Renee Zellweger averts this in the Bridget Jones movies. Her British accent was reportedly so convincing that when she reverted back to her natural Texan one after the first film wrapped, somebody asked why she had adopted such a "phony American accent."
Channing Tatum couldn't seem to make up his mind whether he had an accent or not in The Eagle. It goes back and forth from vaguely British to American. One can only assume he was going for The Queen's Latin.
Happens in Your Highness. As they enter the labyrinth, Thaddeus speaks a sentence in a clear "standard American" accent, as opposed to the British one he had the rest of the time.
In Scream 2, Randy inexplicably has a faux-British accent during his first scene.
Parodied in The Producers (the remake) when Max Bialystock calls himself O'Bialystock and fakes an Irish accent, which gets progressively worse as he continues talking.
Max: And now I'll be on me way, before me voice gets any higher!
Al Pacino's accent in Carlito's Way goes from a slight Puerto Rican accent to normal Pacino accent to Scent of the woman accent.
In Dr. Strangelove, British Peter Sellers' portrayal of American President Muffley noticeably lapses into English pronunciation during the doomsday scene. The supposedly Soviet Ambassador (played by the also-British Peter Bull) was a lost cause from the beginning.
Speaking of Brosnan, his usually convincing English accent slips frequently in the hospital scene of Die Another Day. Particularly obvious examples are his liquid consonants in the lines "I never ask to be traded" and "number one is no deals", and pretty much any instance of the unrounded "A" sound (as in "partner"), as well as a few other vowels.
Toby Hemingway is British. His character Oscar in Feast Of Love is American. His accent wavers a bit sometimes, particularly in the scene of Oscar and Chloe in Oscar's bedroom, where they discuss his past.
Miley Cyrus had to get a vocal coach to keep her from using her natural Tennessee accent (although, it seems to be less noticeable since she's moved to Los Angeles) in The Last Song. While she generally managed to not sound Southern, she never managed to keep any sort of New York (where her character was from) accent for long and in some scenes you could definitely hear her true accent, usually the more emotional ones. The Australian Liam Hemsworth who plays Miley's character's Georgian (as in the state, not the country) love interest, seems to avoid this trope entirely, though.
Sir Alec Guinness in Cromwell as King Charles I. The character deliberately puts on an English accent to cover up his natural Scottish accent. The Scottish comes out when the character gets angry or isn't surrounded by courtiers. This can be considered a case of Fridge Brilliance because Charles I was actually Scottish - born when Elizabeth I was still alive and his father was just the King of Scots, he moved to England at age three.
Simon Baker struggles with his American accent at times in Margin Call. He doesn't quite slip back to his native Australian, but he acquires an odd brogue for some lines.
British actress Emily Lloyd's Brooklyn accent in the 1989 film Cookie was considered so poor that, for the next movie where she played an American, In Country, she went to live with a Kentucky family for a long time before shooting started. As a result, her accent in that film was much better.
In Who Framed Roger Rabbit, Englishman Bob Hoskins does a fantastically convincing New York accent for the character of Eddie Valiant (which is strange, as Valiant lives in Los Angeles, but then East Coast is probably an easier accent for the British to do than Californian). It only slips once: when Roger hides in his desk drawer, Eddie screams "GET OUTTA THERE", sounding very British. (It's not the pronunciation so much as the inflection; most Americans would put the emphasis on "outta", but Eddie puts it on "there")
Matilda: Playing Miss Honey, South African actress Embeth Davidtz is absolutely unable to convincingly fake an American accent. As with the Roger Rabbit example above, at times her inflection gives the game away, such as her use of "NO-b'dee" instead of "NO-buddy." (Even worse, Davidtz is actually American by birth.)
Fridge Brilliance sets in, however, because she was raised by her cruel aunt, Miss Trunchbull, who is British and may have influenced Miss Honey's hodgepodge of an accent.
Mrs. Wormwood's ear-grating Long Island Affect also fades out at times (Rhea Perlman only has a slight Brooklyn accent in real life.)
In Safe House, Irish actor Brendan Gleeson plays an American CIA higher-up. His accent is not particularly convincing.
Rachel Weisz's American accent in The Fountain is, for the most part, passable, but there are moments it goes straight up her nose.
Christopher Lambert had trouble being convincing with Connor Macleod's Scottish accent in Highlander, due to trying to use it on top of his natural French accent.
Word of God is that Lambert didn't speak much English during the filming and memorized his lines which were transliterated for him.
For that matter, Sean Connery's attempt at playing a Spanish Immortal results in a very Scottish-sounding Spaniard.
In the 2011 film Warrior: In the scene where Paddy visits Brendan for the first time, Joel Edgerton's Aussie accent slips out when he says "I've got a wife and kids; I don't have time for whatever this is." (It's adorable.)
In Fight Club: in the scene near the end where the protagonist tries to explain the Tyler situation to Marla, Marla says: "I tried Tyler...", and Helena Bonham-Carter slips into her native accent when she pronounces the name; she noticeably aspirates and broadens the starting vowel.
German actor Horst Buchholz pulled off a credible Polish accent in most of Tiger Bay, only to stumble when his character started yelling near the climax.
In Les Misérables (2012), Sacha Baron Cohen's accent is all over the place. Possibly intentional, as he's playing a con artist who adopts several identities over the course of the story. In particular, his occasional French accent (the only one that any actor in the film attempts, even though the film takes place exclusively in France – note everyone else speaks with a British accent.) is clearly an affectation that the character adopts whenever he wants to sound "classy."
Crowe brings a sleazy, blustering charm to the part of the villainous mayor, even if his accent racks up frequent flyer miles careening between New York, Boston, and Sydney.
Aliens. Carrie Henn, who played Newt, was living in the UK at the time of filming (one of her parents was British, the other American), and apparently picked up some of the accent. Near the end when the protagonists are escaping through the airducts, she suddenly slips into an English accent on this line:
Newt: Up there! There's a shortcut across the roof!
In G.I. Joe: Retaliation Ray Stevenson's accent goes from Southern, to Cajun, then to quasi-Australian in a few scenes.
James Van Der Beek makes a complete unconvincing Texan accent in Varsity Blues.
In sex, lies, and videotape, Laura San Giacomo's apparent difficulties in covering up her native New York metro-area accent with a Southern drawl result in her either barely using it in some scenes, or overdoing it slightly in others.
In Ghostbusters (1984), both Dan Aykroyd and Harold Ramis fail to conceal their natural accents in various places. Egon Spengler sounds awfully Chicagoan for an Ambiguously Jewish character supposedly born and raised in Cleveland and currently living in New York, and for all intents and purposes, has probably been living in New York for several years. Similarly, for someone purportedly born and raised on Long Island, Ray Stantz sounds very Canadian. It's notable at the end when Ray's apologizing to Peter for his "barbecued dog hair" comment; "sorry" comes out as "soary" as it does at various other points in the film.
Sharlto Copley as King Stefan in Maleficent. While the film's setting is not explicitly stated (the novelization says Scotland, but the film itself makes it out to be a standard fairy tale medieval kingdom), everyone has some kind of British accent. Copley, a South African, does his best to sound Scottish, but viewers were not entirely convinced. Especially noticeable since his wife In-Universe, Leila, is played by British actress Hannah New, who naturally has such an accent, while his daughter, Aurora, is played by American actress Elle Fanning, who manages to sound convincing enough.
In Whip It, Alia Shawkat's difficulty in maintaining her Arabic accent audible in some of her deleted scenes resulted in director Drew Barrymore instructing her to speak in her natural American accent for the remainder of filming.
The Wolf drops his British accent completely once he starts singing.
The Witch seems to switch between British and American at certain points in the film.
Lucy Punch sounds virtually American when singing, but retains her natural British accent when speaking. Considering all the other actors portraying the characters in the Cinderella story are American, this was probably an attempt to avoid standing out.
In Big Eyes, Christoph Waltz's own Austrian tones sometimes come through, particularly when he's shouting, such as in the scene when Margaret confronts Walter about "S. Cenic"'s name being on the paintings that he claimed he did.
In the B-MovieWerewolf (featured on MST3K) both the love interest Natalie and the antagonist Yuri gain and lose multiple accents throughout the movie. This—and the the dialog's bad grammar—culminates in the riff:
Tom Servo: (imitating Natalie) Paul! You is a waar-wilf!
The 1997 Batman & Robin film had American actress Alicia Silverstone play a supposedly English character. Unfortunately, her accent was not at all convincing.
That implies she was attempting one at all.
Mel Gibson's mixed accent sounds slightly Australian throughout the first Lethal Weapon movie, especially on vowels and when he raises his voice. However, you could argue that it is in-character, since it's perfectly logical that Riggs could have spent some time in Australia. It's faded by the third and fourth movies.
Jennifer Lawrence and Josh Hutcherson in The Hunger Games occasionally speak with their native Kentucky accent. However, this is completely logical since District 12 is supposed to be in the Appalachian coal-producing region, i.e. Kentucky and West Virginia, and this may in fact have been intentional on the part of filmmakers.
While Irish-born Colin Farrell can do a very convincing fake American accent, in Minority Report, his character Danny Witwer mentions seeing his father get "shot on the steps of our church in Dublin". The line had been added in as a failsafe if Farrell's accent slipped.
Examples in which this trope is in-character:
The James Bond film For Your Eyes Only (see top quote). The title of this entry comes from Silent Hunter misremembering the line from it. Lisl is actually a Liverpudlian lady pretending to be an Austrian countess. Bond still sleeps with her, because he's James Bond, ferchrissakes.
Inverted in Casino Royale (1967): Agent Mimi, played by the Scottish Deborah Kerr, impersonates M's widow, but upon witnessing the prowess of David Niven's Bond, doesn't lapse back into a native French accent, but starts singing his praises in orgiastic French.
In Shadow of the Thin Man (1941), high-class prostitute Claire Peters usually spoke with a pronounced "posh" British accent (or at least what sounded like one to Americans). But when frightened or angry, she would slip into a lower-class New Yorker accent. Nick catches her doing this in one scene.
In Cromwell, King Charles (Alec Guiness) disguises his Scottish accent, until one scene where he memorably loses his cool. Of course Charles's father was Scottish so it seems reasonable his son might have picked up traces of it despite spending the vast majority of his life in England and being surrounded by people actually born there.
The British Michael Caine played a Maine doctor in The Cider House Rules. In case his accent slipped, the director justified it by having the doctor mention his mother was an immigrant.
In Gosford Park, American Ryan Phillippe plays a character who is supposedly Scottish, but the actual Scottish main character (played by Scottish actress Kelly Macdonald) recognizes it as fake immediately.
Layer Cake has this with Eddie Temple (played by Michael Gambon), that's a combination of this and the first type. Gambon's character often speaks with a plummy English accent, and the director's commentary mentions his complaint about difficulty holding the accent. The director told him to let the accent slip at will any time he felt like it, which fits the character well, a London Gangster who has moved into high society and taken elocution classes. In particular, his posh accent tends to slip when the character is angry.
In Velvet Goldmine, Toni Collette plays an American woman who moves to England and subsequently develops a British accent. In flashbacks, her accent slips when she's upset; in scenes taking place in the present, she doesn't bother. It's particularly impressive given that the actress is Australian, therefore neither of the accents she veers between are her own.
This is actually a positively uncanny imitation of Angela Bowie, who is American but either absorbed or intentionally adopted a faux-British accent during her then-husband's glam rock days. It's especially prominent in the opening to Ziggy Stardust: The Motion Picture, for example, when she comes backstage to chat with the band.
A deliberate regional-American-accent example occurs in The Wizard of Oz, when the fortune-telling huckster speaks to Dorothy in the tones of an educated East Coast man, then slips into a rustic vernacular to talk to himself after she's left. Beautifully done by Frank Morgan.
In Tenacious D in The Pick of Destiny J.B. when falls prey to the street gang that is a Shout-Out to A Clockwork Orange. Its members speak with mocked-up British accent and when one of them utters a phrase with actor's natural accent, he is promptly punched to the chest by the leader and returns to the mocked English.
In Pacific Rim, Pentecost's accent goes on and off depending on his tone of voice, indicating that his heroic front is, to some degree, a facade. He drops it entirely when he tells Raleigh about the radiation poisoning.
Part of the Reveal in the movie Gotcha! While argue about whether she used him or not, Sasha's accent slips and drops completely when she admits she isn't from Czechoslovakia.
In 7 Faces of Dr. Lao, the eponymous wizard casually slips back and forth between speaking with a heavy Chinese accent and deploying perfect English diction, a fact which is explicitly noted by one of the other characters and lampshaded:
"Oh, it comes and goes. Whatever dialect the mood requires."
Sebastian Stan has mostly done away with his original Romanian accent, but you can hear it very slightly in The Education of Charlie Banks when he says "I'm way too hungover for a lecture" right before Mick (Jason Ritter) beats him up.