Her Mancunian accent in Steamboy slips from time to time.
Many early Manga Entertainment dubs had British actors putting on American accents with varying degrees of success, often so bad it's hilarious. These also included colloquialism failures, such as saying "knickers" instead of "panties" (for women's underwear), etc.
Lifelong Doctor Who fanboy David Tennant, before being cast as the Tenth Doctor himself, was cast in several Big Finish Doctor Who audio plays—at the time, the only new dramatic Doctor Who being produced. In one play, "Colditz", he played an evil Nazi. The very Scottish Tennant preformed his role with a very German accent, and only slipped once: "I vil do my" (in a massively Deutschland accent) "DOOOO-ty!" (sounding nothing so much like the most stereotypical Scotsman you have ever heard).
The audio book of the Doctor Who novel "The Coming of the Terraphiles" is read by Clive Mantle, whose struggles to reproduce Amy Pond's Scottish accent result in him sounding not entirely unlike Mrs Doubtfire.
Deliberately invoked with Hank, American Alfred to the British Batman in Knight & Squire. In the text piece, Paul Cornell says he imagines Hank as being played by an actor from Milton Keynes, with an accent that wanders all over the place, just like American characters on British TV when he was a kid.
In-universe example in The Sandman, where a Chinese character switches between speaking perfectly good English and "Solly, no speakee English" by way of Obfuscating Stupidity.
Many of the characters in Preacher speak turn of phrases decidedly not American/Texan and more Irish (writer Garth Ennis' homeland). These are usually funniest when the main character is written with his typical Texas drawl saying them.
When Cassidy has to fake a Texan drawl, he slips up, and gets called on it - not by the bad guys, but by Jesse, who figures Cassidy only got away with it for as long as he did because he was talking to a German.
In a blink-and-you'll-miss-it bit of foreshadowing, Molly Hayes of the Runaways, during a fight with a group of deluded former teen heroes who've been hired to shut the Runaways down, comments that Chamber's British accent sounds fake. It's later revealed that he's not Chamber, but a mole from the New Pride.
In an early Nero Wolfe novel (Over My Dead Body), the suspect Madame Zorka, exotic foreign fashion designer, always used an incredibly thick Pottsylvanian accent. Until, of course, her real identity was discovered - Pansy Bupp of Ottumwa, Iowa - whereupon she collapsed into a Midwestern American accent. (After all, is High Society going to patronize a fashion designer from Iowa?)
In a recent novel about the murderer Crippen, an upper-class woman was revealed to be a lower-class social climber when she got angry and said, "He's very handy with his dukes!"
In Night Watch, Edgar usually speaks with a perfect Moscow accent, but tends to slip into his native Estonian accent when agitated.
Terry Pratchett's Discworld has many characters whose accents slip - the younger Igors occasionally forget to lisp, and Doreen Winkings (aka the Countess Notfaroutoe, a vampire by marriage) has an Uberwaldian accent far thicker than any native Uberwaldian, except when she forgets.
In the Gaunt's Ghosts novel Blood Pact, when Baltasar Eyl Damogaur catches up to Gaunt and Mabbon for the last time, he goes back to his natural outworld accent, having difficulty maintaining his civilised veneer.
In "The Queen's Thief" series, Eugenides fakes an Attolian accent and no one even thinks to look for his Eddisian one (despite knowing he's Eddisian) until he slips because he's talking in his sleep.
This was a key plot point in a Nancy Drew Case Files mystery. A supposedly American man said that someone was "in hospital" instead of "in the hospital", and used other Britishisms, leading Nancy to suspect that he wasn't who he claimed to be. It's capped off during a scene in which he gets into an argument (a classic "highly emotional scene" as mentioned in the page description), when he suddenly begins speaking with his British accent.
Sally Pyne's "Lady Sarah" accent in Aunt Dimity and the Family Tree "hovered precariously between the queen's and a fishmonger's." Willis Sr. could only say of it, "I cannot bring myself to discuss her accent except to say that it is strikingly original. I do not believe that it has ever been heard before on this or any other planet."
Shadwell in Good Omens has an accent which seems to be on a tour of all the least mellifluous regions of the British Isles.
In the dialogue sections of the music video for the Genesis song, "Jesus He Knows Me", Phil Collins is playing the part of an American televangelist from the Deep South. At first, Collins, born in the West London district of Hounslow, manages the accent well, but as it begins to slip it almost comes out as Irish-sounding!
Hilariously lampshaded in an episode of WWE Raw. The Ghanaian-American Kofi Kingston has been portraying a Jamaican character, complete with the stereotypical accent. In the episode in question he inexplicably speaks in his American accent during a promo, and the ever-JerkassWith a Heart of GoldTriple H just had to call him out on it.
Doubling as Hypocritical Humor and Hilarious in Hindsight as Trips originally tried a French accent earlier in his career, failed and settled on just being New England though the intention was to flesh out Kofi.
King Booker uses an obviously put-on fake aristocratic British accent and returns to his Booker T-ish way of speaking when sufficiently riled or angry.
The Broadway production of the musical Spamalot plays with this — the usually good British accents are sometimes dropped for comedic effects on certain lines, like "you are so gay" after Lancelot's angry outburst in the castle.
When popular West End Elphaba Kerry Ellis transferred to the Broadway production of Wicked, she seemingly could not decide if she was playing an American or a Brit, her accent wavering seemingly every other sentence.
The Broadway Cast of The Secret Garden seemed to have had a good dialect coach and try very hard, but unfortunately can't really carry the Yorkshire accent. Those attempting RP have more success.
The 25th anniversary English cast recording of Les Misérables featured factory workers who seemed to wander from Cockney to 'generic northern accent' to Irish in the same phrase. Fortunately it only really happens in At the End of the Day.
In Vanities, Mary and Kathy both drop their Texas drawl for generic accents in the third act. In some productions, Kathy acquires a New York accent. In the HBO version, they kept their accents, although less strong than before. In the added scene of the musical, Joanne may lose her accent as well.
In a Carnegie Hall performance from 1962, Julie Andrews and Carol Burnett sing a cowboy-themed duet called "Big D (Dallas)"; Julie's attempt to sing with a Texas draaaaawl is arguably just as embarrassing as the fake-Cockney that Dick Van Dyke would do a year later in Mary Poppins.
Gamila in Pilgrims Musa and Sheri in the New World slips between an American accent and her native Arabic accent. Justified, as she attended an American school in Egypt.
In the Donmar Warehouse production of Cabaret (as seen in the 1993 TV movie), Adam Godley is a very American Cliff Bradshaw. Until he gets upset. Then he's a very Irish Cliff Bradshaw. Made even stranger by the fact that Adam Godley isn't even Irish to begin with.
In-story example: Faye from Questionable Content hides her Southern accent because she believes it makes people think less of her. When she gets angry, she even stops using contractions. However, when she gets drunk, the act flies out the window.
Anja Donlan of Gunnerkrigg Court is Romani and not a native English speaker. By adulthood, her English is so good that you wouldn't be able to tell, but in one flashback she slipped a bit while crying over the death of a friend.
When his love interest gets stabbed, Higgs of Girl Genius starts to slip into a Germanic accent. This one is complicated, since Translation Convention is in effect: Everyone is speaking German, but its only the jägers who are written with the accent.
The Jägers all have enormous fangs instead of teeth (even Maxim, who is as close to bishonen as you can get without having your personality surgically removed), with the implication that the "accent" is more like a speech impediment caused by trying to talk around their ginormous choppers; Higgs, however, has apparently normal human teeth, so it remains to be seen exactly what the deal is with that.
The Jägers are all much older than they look, suggesting their accent is really a more archaic form of the local language, raising interesting possibilities for Higgs. He remembers old Heterodynes, after all.
Aside from which, Mechanicsburger accent/Jägersprach is not really German; it's more Slavic-Romanian in intent. Lingua europa, the common language the story is presumably translated from, is a creole based on German, but it's nobody's native language.
Jareth in Roommates speaks normally (with a slight british accent, and not too specic font) but reverts to the Foreign-Looking Font other Scandinavian-Germanic / Magical characters (like his father the Erlkönig or Odin) use when he is really angry. Seen here.
In early episodes of Yu-Gi-Oh! The Abridged Series, Yugi's accent in particular had a tendency to wander, most notably in the episode where he meets Mako Tsunami. It's gotten quite a bit better since, though there are some telltale signs if you're paying attention (notably, over-pronouncing the letter "t" and enunciating the "g" at the ends of "-ing" words).
That is probably Hypercorrection due to the fact that British accents often drop or slur those sounds and so he over-emphasises them to sound more American, even if they're not actually emphasised that much in American.
Perhaps a bit forgivable because LittleKuriboh plays almost every character and each of them has a different, equally ridiculous voice and "accent". If you listen to the first episode with the original voices and the first episode with the newer, redone voices, they're remarkably different.
Lampshaded in episode 48. Yugi has a flashback to his accent slip-up in the Mako episode, referring to it as the time he inexplicably started talking in a British accent. Naturally, flashback!Yugi's speech degenerates into a list of stereotypical British terms.
And again in the Alternate Episode 6.
Yugi: Remember when Li'l Kuriboh could barely voice-act? That's what's 'appenin' now gov'nah
In The Slayers Abridged, Zangulus has some New England dialect that can slip, and Vrumugun's French accent slips constantly. projectshadow99 himself has admitted that he can't really do accents and he really regrets giving Vrumugun a french one.
In the revised versions of the first few episodes, Zelgadis was going to have either a British or Irish accent, simply because ps99 wanted to try one. This was dropped when he realized he couldn't do those accents either.
Just for the hat trick, Tenchi in Tenchi Muyo Abridged slips into British a lot. Eventually he just got comfortable with it, and it's part of their version of the character. The fact that the dialog has British shibboleths doesn't hurt either.
In Corrupting the Classics with Contemporary Crap episode 3, when the contestants on Project Playwright threaten to leave, Heidi Klum says "But you can't go!" On those last two words, Gwenevere Sisco's natural American accent reveals itself. Probably done intentionally for comic effect.
Strong Bad of Homestar Runner had a slight Mexican accent in his early SB Emails, which has disappeared gradually over time. This is parodied in a bonus sbemail when Strong Sad predicts how Strong Bad's accent will sound several years in the future, showing Strong Bad speaking without the gravelly quality his voice usually has in addition to completely lacking the accent.
Tobuscus is a man of many voices and accents, as evidenced throughout his work. Too bad he seems incapable of remaining in them for very long. He has also been told by genuine Aussies and Brits that his imitations of their accents are awful.
The Critic himself had his accent fade out whenever he was doing positive stuff, letting Doug's real voice come through. He got much better though, and now the only time Doug drops the voice (in-costume) is for bloopers.
From the same website, comic reviewer Linkara's new show "Longbox of the Damned" has this in spades
MovieBob usually does his reviews in a standard American accent, but when one of his Berserk Buttons get pressed, he quickly devolves into his native, thick Boston accent.
Linka of Captain Planet had a tendency for her "Eastern Europe" accent to slip all over the place.
Gi had a vague Asian accent that slipped on and off for the first few episodes, but was then basically abandoned.
Regular Show's future Mordecai and Rigby talk with fake British accents up until they begin panicking; at which point they talk in their normal voices.
"Joust Like a Woman," a 6th-season episode of King of the Hill, uses the trope in reverse. Guest star Alan Rickman voices a Renaissance Fair owner who speaks with an exaggerated British accent until he gets sued by his female employees; then he lapses into his native Texas drawl. An example of a real Brit playing a Fake Brit and a Fake American.
In "A Beer Can Named Desire", when Bill introduces his friends to his extended family in French, he pronounces their names in a French accent, except for the last one: Boomhauer.
G.I. Joe character Destro has always been Scottish, but when it comes to G.I. Joe: Renegades, it seems nobody noticed that Clancy Brown was actually doing an Irish accent all the way through the first season. Realization seems to have come about for the finale, where Brown suddenly started adding an exaggerated Scottish inflection to some sentences, and spent the whole episode oscillating back and forth between the two accents.
Example without really using accents: Andrea Libman voices two characters in My Little Pony: Friendship Is Magic, energetic Pinkie Pie and soft-spoken Fluttershy. When Fluttershy has a musical number in the episode "The Cutie Mark Chronicles", Libman apparently has trouble keeping the character's voice consistent when she's supposed to be very excited, with the end result that she sings the second half of the song basically as Pinkie Pie.
Which is a bit odd, since she doesn't do Pinkie Pie's singing voice, only Fluttershy's.
Tabitha St. Germain voices Rarity and Princess Luna. In "Luna Eclipsed", while Princess Luna normally sounds very royal and high standing, there are a few lines that make Princess Luna sound almost exactly like Rarity. Although, both characters happen to be Large Hams. Even stranger is that Rarity doesn't even appear in the episode at all, as her scene was cut.
Rarity's accent slips occasionally too. In this case it adds to the effect, since it's that high-classy sort of American accent that doesn't actually appear anywhere in nature, and it adds to the impression that it's another thing she's doing as part of her "image" as a fashion designer, but hasn't quite got the act down yet.
Same goes for Ashleigh Ball (the voice of Applejack and Rainbow Dash) during the "At the Gala"-Song in Season 01, Episode 26 ("The Best Night Ever"). She seems to have problems singing in Applejack's heavy southern accent, as well as getting Rainbow Dash's rough voice and her singing together at the same time.
One-time character Pipsqueak, a young colt celebrating Nightmare Night for the first time in Luna Eclipsed, is introduced with a British accent, but by the end of the episode seems to lose it.
The Tom and Jerry cartoon "Robin Hoodwinked" has Tuffy speaking with an ear-bleedingly bad English accent.
Billy: (to Irwin) Why're you talkin' funny? Irwin: (Indian accent) Because I am from Calcutta, in the mystical east. Billy: No, you're not, you live down the street, and what's with that weird thingy on your head? Irwin: (drops accent; shouting) IT'S A TURBAN! IT'S WHAT I WEAR! I'M IN CHARACTER, YO, SO WHY DON'T YOU JUST GET OFF ME!!
The Beatles' manager Brian Epstein took umbrage to Paul Frees and Lance Percival voicing the group on their Saturday morning cartoon show (which Al Brodax imposed so the boys could be understood by American audiences) that he ordered the cartoons to never be shown in England. Lance Percival (Paul and Ringo) was an actual Briton, but Paul Frees' attempts (John and George) to sound Liverpudlian were not incredibly successful.
X-Men (the animated series) was recorded in Canada, so occasionally the actors would slip up. It's especially noticeable for Jubilee, who usually pronounced "Sorry" like "Soh-ry".
In Rudolph the Red-Nosed Reindeer: The Movie, Eric Idle voices Slyly the arctic fox who speaks in a Brooklyn accent, occasionally Idle's natural British accent will slip out.
In the Cowboy Bebop dub, the "Mexican" accent of the male host of Big Shots constantly wanders all over the place. It's finally confirmed as fake near the end.
In Preacher, Cassidy poses as Jesse and temporarily hides his thick Irish accent under a shoddy Texan one. Once his captors find out it's just a ruse and he's not the man they need, the Big Bad quotes this trope. Later on, after Jesse rescues him, he's quite upset at the poor quality of Cassidy's 'Texan'.
Ironically, you can occasionally catch Jessie Custer slipping out of his native texan accent into writer Garth Ennis' Irish one. "Give it here" as opposed to "give me that."
Ennis does it in his run on Punisher, too, with New York-born and bred Frank Castle saying "I've news for you" and "You passed out straightaway". Granted, this was during the "Kitchen Irish" arc, so maybe Ennis subconsciously got caught in a rut.
Also, it's lampshaded in the comics in a conversation between a disfigured IRA bomber and his partner in crime, an American gun runner of Irish descent (who fakes an Irish accent when talking to the IRA guy). The bomber literally has to tape what's left of his face in place. When the gun runner asks him if it slips, the bomber responds "Like your accent?".
It also happens here and there in Transmetropolitan—various City-born characters bust out with turns of phrase or sentence structures more suited to Warren Ellis's English origins.
This can be excused by the fact that, although The City is essentially American, it's portrayed as a conglomeration of many different major metropoli; with a highly international population, mixed and matched over many many years from the present. It quite obviously incorporates a considerable amount of London, as well as New York and Paris; with a fairly idiosyncratic location (it seems to be a coastal port city, with a close proximity to a major mountain chain). Many of the characters have what appear to be deliberately mixed accents.
In her civilian guise, Empowered affects a patently false Southern drawl. Also the villain Rum, Sodomy and the Lash (formerly a trio) who Emp describes as an "underinformed anglophile doofus".
In a Look-in comic adaptation of Street Hawk, Jesse goes to Barbados to enter a motorcycle race as part of an undercover assignment, posing as a Canadian. Unfortunately one of the bad guys really is Canadian and sees through it...
Bizarre in-universe example with recurring villain Padan Fain in The Wheel of Time. The Fain seen through most of the series is actually a composite being of the original Padan Fain and the ancient, undead Evil Chancellor Mordeth, who attempted a Grand Theft Me on him and only partially succeeded. The resulting being tends to switch back and forth between Fain's and Mordeth's accents, almost always unwittingly and sometimes in the middle of a sentence. This generally creeps out anyone who talks with him for an extended time, to greater and lesser extents.
In Beauty Queens Shanti has a carefully cultivated British Indian accent. When she gets scared, she reverts back to her Valley Girl accent.
Capt. Marian Alston in Island in the Sea of Time is a self-educated black woman from the Sea Islands of South Carolina who usually maintains a very precise accent and occasionally slides into a mild southern one. If things get stressful enough (which takes some doing) she lapses into full-blown Geechee.
In The Price of the Stars, Beka Rosselin-Metadi is essentially introduced grumbling to herself about how, despite seven years of earning her living as a starpilot for hire and avoiding anything resembling polite society, every time she gets a few hours short on sleep she starts sounding like she just stepped out of a Central Worlds Finishing School. It proves plot-relevant when a Space Force officer notes the same accent coming from a one-eyed male gunslinger from a frontier system after an all-night running battle about eight months after Beka's supposed death.
Mockingbird princess: Besides, they're useless if they starve to death. Mockingbird guard: Your fake Southern accent is slipping again, princess. Mockingbird princess: T'ain't fake! Ah jest, ya know, plumb ferget Ah got it... sometimes.
Faye from Questionable Content is from the South (in a strip set in Massachusetts). For the most part, she tends to assimilate her accent, but it can be heard (er, read) when she's been drinking or very angry.
In The Order of the Stick: the vampire possessing Durkon has been speaking in his accent to pass among the Order without suspicion. He notes in a private scene that he's slipped up on the accent a few times, but no one's noticed.
An odd, non-aural example occurs in Survival of the Fittest. Maxie Dasai speaks with a notable accent, however, this tends to vary from topic to topic as the handler forgets older verbal patterns or comes up with new ones. Funnily enough, it isn't that noticeable.
The To Kill a Mockingbird videos on the BBC Bitesize website feature British actors that can't seem to decide whether to speak in Alabama accents or their natural English ones.
Ross on Steam Train is from Australia, and sometimes slips into an Australian accent (especially when he's tired). However, he denies that he has an Australian accent, and claims that he didn't have one even when he lived in Australia.
Ultra Fast Pony. Spike normally has an Igor-esque German accent, but in "Utter Lunacy" he disguises himself by faking a Jamaican accent (as part of a Paper-Thin Disguise). He briefly slips back into his normal accent, nearly giving himself away.
In early episodes of The Hardcore Kid, Brandon Nichols's voice would slip in and out of a Fake Brit accent when playing Mr. British Guy.
In Transformers Animated, Shockwave speaks with a slight David Warner-esque British accent, but his alter-ego of Longarm has an American accent.
Shockwave's voice actor is well known for doing a range of different voices. You might also notice that the Transformers Animated Shockwave sounds exactly like his G1 cartoon counterpart - because the same voice actor from the 80s cartoon came back to play him!
In The Simpsons episode "Life on The Fast Lane", Jacques speaks in a faux-French accent which slips when he yells at the bowling alley waitress for more onion rings.
On WordGirl,Tobey always speaks with a fake British accent during his evil plans, but it dissolves into an American accent when his mother shows up to stop him.
The Legend of Korra: Mako has only a slight Brooklyn-ish accent around people he doesn't know personally (Korra, Butakha), but it gets heavier when he talks to Bolin or other street kids.
In Young Justice, Blue Beetle speaks with a noticeable Spanish accent, which starts slipping "The Runaways". This turns out to be a plot point, not his voice actor messing up, since it's really the Scarab in control of his body.
Mr. Herrera, the Spanish teacher on Beavis And Butthead, speaks with a thick Mexican accent until the duo irritate him enough to lose it.
In My Little Pony: Friendship Is Magic, as part of a desperate attempt to woo a visiting travel writer, Rarity adopts and exaggerates the mannerisms of her friend Applejack, right down to an over-the-top Southern accent. That said, one can tell that she struggles to maintain it, allowing her normal "Mid-Atlantic" affectation to slip through to much hilarity.
The astute listener to CBS News could always spot when a particular breaking story had been going on too long: during Election Night 2000, for example, when Dan Rather's assumed Network Standard accent began seriously slipping out of his control and revealing his Texan roots.
Another strange case from Supernatural, Lauren Cohan. She was born in America but went to school in England, and her natural accent is a mix of the two. She went full British as Bela Talbot, and had one scene where she went full American as a reporter.
Lyse Doucet, a reporter and presenter who has been with the BBC News servicefor quite some time, was born in Atlantic Canada. She has a very distinct way of annunciating that, when she's reporting for an American or Canadian audience, tends toward US/Canadian news TV standard; sounds more Estuary when she's on the BBC; and is nothing like the accent she grew up speaking or tends to when she visits her home town in New Brunswick.
The Japanese language has a heck of a lot of loan words, where a language borrows words from another language for which it has no equivalent. For example, the English word "computer" is a loan word. However, because they have a specific phonetic structure, you have to say it like "konpyūta" for them to understand it. So, even when using English words, they won't understand your accent unless it's Japanese. This is an easy way to tell native and non-native speakers apart.
Also, they tend to say "Pasokon" (Persocom), short for "Pāsonaru Konpyūta" (Personal Computer), or just "Pī Shī" (PC), which might add to the confusion if you just say "Konpyūta" to them.
Other words that get this include "chocolate" (chokorēto), "orange juice" (orenji jūsu) and "ice cream" (aisu kurīmu). Note that some of these are a bit ridiculous; the orange, for instance, is actually native to East Asia and was known to the Japanese well before the global influence of English came along.
They've been at it for centuries. "Tempura" is a loanword from Portuguese ("tempora", time of year, referencing e.g. Lent), and others can be found here. The Portuguese influence dates to the 1500's.
Most words which are pronounced with the on-reading of a kanji have come from Chinese, which appears around the 7th century. The on-reading is a the pronunciation of a Chinese word with a Japanese accent, essentially, meaning they have been at it for over 1300 years.
People who move around often as a child—for example, people whose parents are in the military—often pick up fragments of different accents. No personal examples, please.
The British synth-soul group Alabama3 tends to affect southern US characters for their stage personas. The monologue at the beginning of the original version of "Woke Up This Morning" (better known, remixed, as the theme to The Sopranos) features lead singer Rob Spragg doing a very strange accent — a slightly exaggerated African American accent with painfully British enunciations. The way Spragg comes so close and fails to nail it has to fall into the Uncanny Valley.