The Simpsonsreally suffers from this one about as much as Saturday Night Live does (thanks to both shows being on the air for a long time and having old episodes rerun and/or be available on DVD for newer viewers to discover coinciding with newer episodes still running on their respective networks):
Because a major plot point in episode "The City of New York vs. Homer Simpson" had their car being parked on the World Trade Center's plaza, it wasn't shown much in syndication after September 11th. Lines like "They put all the jerks in Tower One!" didn't help. After 9/11, the writers on the DVD commentary did say they felt bad about that joke in hindsight.
They lampshaded it when they returned to New York a decade later:
Bart: Come on, Dad, you'll love New York now that your two least favorite buildings have been obliterated: Old Penn Station and Shea stadium.
Homer: Lousy, outdated relics
Another 9/11 Aneurysm Moment: the episode where Bart, Milhouse, Nelson, and Ralph become a boy band had a scene where a missile from an aircraft carrier blasts the MAD Magazine building. While "City of New York vs. Homer Simpson" can be forgiven since it was the 1990s and no one even dreamed of that ever happening (except in action movies), the boy band episode aired in February 2001, seven months before the 9/11 attacks would go from being "Ha, ha, ha," to "O.M.G., Too Soon!" One of the writers pointed this out on the DVD.
If the New York episode is the Trope Codifier for the show, the Season 5 episode "$pringfield" is a close second. In this episode, which aired in 1993, two No Celebrities Were Harmed versions of Siegfried & Roy perform an act with white tigers riding unicycles. The act goes horribly wrong when one of the tigers attacks one of the two illusionists. A decade later, a white tiger actually did attack Roy during one of their shows. This moment was lampshaded on DVD commentary and declared the "greatest prediction ever made by The Simpsons," though the writers also pointed out that the tiger attack was bound to happen sooner or later, considering how she was treated.
In the Season 10 episode "Sunday, Cruddy Sunday" (which aired after the 1999 Super Bowl), Nelson asks if the postman has ever gone on a rampage and killed people. The postman remarks that the disgruntled mailman stereotype is a thing of the past. Skinner then replies, "I'm glad I work in an elementary school!" followed by an awkward silence (though the awkward silence could be because no one laughed at Skinner's lame attempt at making a joke). This episode premiered when the trend of kids going ballistic and opening fire at their schools was a hot topic, and with one of the most infamous school shootings of all — Columbine — taking place just a few months after it aired, the joke's darkness gets blacker and a lot more tasteless — and thanks to the Sandy Hook Elementary School massacre in 2012 (which has been reported as the worst school shooting since the Virginia Tech massacre in 2007), the joke is still in bad taste. And if you're British, it's an especially massive Too Soon or Dude, Not Funny! because of the Dunblane school massacre (in which a gunman entered a school and shot 16 children, one adult and then himself, which happened 3 years before the episode aired).
In the closing credits of the clip show "All Singing, All Dancing", Snake is heard shouting "Stop the music!", and he fires his first gunshots as Phil Hartman's name comes up. Four months after it first aired, Hartman was shot to death by his wife in a murder-suicide.
There's also the scene in "Marge vs Singles Seniors Childless Couples and Teens and Gays" where Bart wants to watch a TV show where Steve Irwin gets mauled to death by an animal (although it is a crocodile that kills him on The Simpsons).
There's that episode guest starring Mel Gibson (season 11's "Beyond Blunderdome"). He was complaining that people like him too much, and ends up creating a movie so controversial that everyone hates him. Funny how life imitates art, no?
A lot of the earlier episodes had verbal jokes and sight gags depicting Homer as a monkey (and often being called a "big ape" due to his crass behavior and informed ugliness). These stop being funny with the episode "The Color Yellow," which reveals that one of Homer's ancestors was a black slave (and for the uninitiated, "monkey" is [or, at least, has been] used as a racial slur against black people).
Then there's the line in "Weekend At Burnsie's" when Homer (who's been smoking medicinal marijuana after getting pecked in the eyes by crows) states that he can go up to The President and "...blow smoke in his stupid monkey face, and he'd be sitting there groovin on it!" This episode was written and premiered around the time that George W. Bush was U.S. President (and there were a lot of jokes about George W. Bush looking like a monkey because of his big ears and simian-looking face). These days, with a black president, that line comes off as horrifically racist (and it doesn't help that Obama himself has large ears as well).
Homer sees a movie called "Hail to the Chimp" at the drive-in theater on the season nine episode "Dumbbell Indemnity." Very Hilarious in Hindsight during the "Dubya" Bush era; totally racist in the Obama era.
The climax of "Deep Space Homer", with fears of the shuttle burning up in reentry, is wince-worthy in light of how the Space Shuttle Columbia burned up in its reentry in 2003.
In "Lisa's Date With Density", Lisa asks Milhouse to send Nelson a love note from her, but Nelson is led to think the note's from Milhouse himself. Cut to Milhouse being led away in a stretcher to an ambulance (with the paramedics telling Lisa that Milhouse can't hear her — not because he's dead, but because his ears are packed with gauze). It really stops being funny after the highly publicized rash of suicides and murders from bullying, especially anti-gay bullying. The setup of the scene is horrifyingly very similar to the murder of Lawrence King in 2008.
The same thing applies to the flashback of "Bye Bye Nerdie" where a school-aged Homer is shown beating up a school-aged Smithers (who, in later episodes, was established to be gay and not just have a man-crush on his boss like in the early episodes) who's wearing a pink shirt and shorts to the tune of "Kung-Fu Fighting." These days, Homer would have been expelled for doing that.
Due to the rise of youth violence (including bullying and suicides from teens who have been harassed), episodes like "Bart the General", "Bye Bye Nerdie", "The Boys of Bummer" and "Lisa's Date with Density" (though just the "note" scene as detailed above) will come off as very disturbing in a world of concerned parents and ostracized children who are or have ever been the target of a bully (though Marge stuck up for Bart in "Boys of Bummer and "Bart the General" did address bullying and violence in a serious manner at the end).
In "Homer Defined", Magic Johnson "pulls a Homer" by tripping while trying to dunk and ending up in the adoring arms of a swarm of cheerleaders. Less than a month after the episode aired, Johnson announced he was HIV positive, which he got from sleeping around with many women.
The season five episode "Lisa vs. Malibu Stacy" has a scene of Grampa stealing Andy Griffith's pills (and Andy Griffith in an ambulance next to him being rushed to the hospital for a heart condition), became significantly less funny after Andy Griffith's death on July 3, 2012, even less so now that it has been determined that his death was caused by a heart attack.
A gag in "The Monkey Suit" has Snake shooting people from atop the Kwik-E-Mart became much more grim in 2011, when a gunman opened fire and killed six people (and severely wounded Senator Gabrielle Giffords) outside of a Safeway store in Tucson, Arizona.
There was a similar gag to that on the season five episode "Homer the Vigilante," only it was Apu shooting a man who was trying to enter the Kwik-E-Mart. Back then, it was supposed to be a reference to what Korean store owners did during the L.A. Riots in the mid-1990s.
In "Burns, Baby Burns", the news shows a computer simulation of Homer walking out of the Aztec Theater and shot to death by the cops. It's a lot less funny thanks to that Aurora, Colorado theater shooting in July 2012.
In the episode "Brawl in the Family" the Republicans meet to talk about what to cut from the budget. Krusty mentions cutting PBS funding because "those lousy Muppets are taking up his airtime". It stopped being funny when Mitt Romney announced he would cut PBS's funding if elected President, and Big Bird appeared in an Obama ad (after news hit about his appearance on Saturday Night Live) attacking Romney for it. It's now Hilarious in Hindsight since Obama got re-elected.
In "The Day the Violence Died", Bart and Lisa complain about Generation X during the Schoolhouse Rock parody, with Bart commenting that "We need another Vietnam to thin out their ranks a little." We did get another Vietnam, only it's called "The Second War in Iraq" (the one started in 2003).
Ditto Moe's line on Homer's Phobia:
"Used to be if you wanted to make a boy into a man you'd send him off to war. But there aren't even any wars anymore; thank you very much, Warren Christopher!"
Made somewhat less tasteless in that the Iraq War did not prompt drafting, the main distinction between Vietnam and successive US conflicts, but still, Vietnam and the second Iraq war were wars that were controversial because of the vague reason for fighting it.
"A Totally Fun Thing Bart Will Never Do Again" centered on Bart sabotaging a cruise ship so his cruise vacation can last forever, which leads to disaster. In February 2013, a similar situation happened to Carnival Cruise Line's Triumph.
In the episode See Homer Run, Rainier Wolfcastle (The SimpsonsExpy of Arnold Schwarzenegger), in a stump speech, mentions that he is among other things, a womanizer. Years later, we have Arnold Schwarzenegger divorcing Maria Shriver because Schwarzenegger cheated on her and had an illegitimate son.
In "Brush with Greatness", Ringo Starr says that he'll take his time to answer every piece of fan mail that he didn't get to answer (including Marge's, which included a painted portrait of Starr). These days, this comes off as either confusing (for anyone who hasn't seen the early episodes of The Simpsons in the 1990s and now are discovering them on DVD or the Internet) or depressing, as Ringo announced in 2008 that he's not accepting fan mail anymore.
On the season seven clip show episode "The Simpsons 138th Episode Spectacular," the original three Simpsons showrunners-cum-creators are Matt Groening (depicted as a gun-crazy redneck), James L. Brooks (depicted as being very fat, very rich, and the winner of several awards), and Sam Simon (depicted as a frail expy of Howard Hughes in his later years). Sam Simon was diagnosed with terminal cancer in early 2013 and is slowly, but surely dying.
In "Bart-Mangled Banner", Elmo is shown in prison as a political prisoner. Eight years later, Kevin Clash (the puppeteer and voice actor for Elmo) was later accused of having sex with underage boys. The case was dropped and he wasn't imprisoned, but it definitely changes the context of the line, "Elmo went to wrong fundraiser."
In "A Star Is Burns" (the Critic crossover episode that Matt Groening hated), there was a scene from Rainier Wolfcastle's horrible stand-up comedy movie where his Woody Allen "impression" is just Wolfcastle saying, "I'm a neurotic nerd who likes to sleep with little girls." Back then, it was a Take That at him marrying his step daughter Soon Yi and was in bad taste. Things got worse, when in October 2013, his adopted daughter Dylan admitted he sexually abused her twenty years earlier.
A deleted scene from "Krusty Gets Kancelled" (which was later featured in "The Simpsons 138th Episode Spectacular") shows Krusty trying to sell a book featuring him in sexually explicit positions in an attempt to revive his show (in the wake of stiff competition). He makes the mistake of trying to sell said book during a taping of his show, where there are children present, and the FBI arrest him during the promotion. ("It's not really me; I used a stunt butt!") It was meant to be a knock on Madonna producing a similar book, as well as a joke about Krusty being a very pathetic showman/promoter. Almost 20 years after "Krusty Gets Kancelled" aired, British TV and radio host Jimmy Savile was posthumously accused of upwards of 218 cases of sexual assault, with allegations that he may have molested children during tapings of Top of the Pops and Jim'll Fix It (the latter was a popular kid's show during the 70s and 80s). As a result, Jim'll Fix It is all but banned forever, and reruns of Top of the Pops featuring him are also unlikely to air in the UK ever again. Whether it was funny or not in the first place, the scene is definitely more awkward now.