The Simpsons is a long-running animated sitcom created by Matt Groening for the Fox Broadcasting Company. The show is the longest-running American animated TV series of all time which currrently still airs to this day, and is considered to be one of the greatest cartoons of all time.
Unlike most FOX shows, The Simpsons takes aim at both the Democratic and Republican parties, depicting Republicans as corrupt warmongers and Democrats as brainless idiots. (and the opposite, indeed!) Not even presidents were safe from criticism, as Richard Nixon, Jimmy Carter, George H.W. Bush and Bill Clinton have all been subjected to mockery on the show.
The Simpsons has many famous celebrity guest stars in their episodes (Ringo Starr, Barry White, George Carlin, Leonard Nimoy, Mark Hamill, Rupert Murdoch, Michael Jackson, Alec Baldwin, etc).
On some occasions, the humor is done at the wrong time and barely makes any sense.
Season 1's animation isn't that great, as it has a ton of errors, washed out colors and mediocre character designs.
"Some Enchanted Evening" is the worst offender, especially the original version of it. Matt Groening and his crew wanted a show with more restricted, less cartoonish animation, while Klasky Csupo wanted something fluid and expressive a la the Tracey Ullman shorts. Nobody seemed to have told AKOM anything, meaning the animation of the episode was wildly inconsistent, and 70% of the animation had to be redone by David Silverman's domestic unit (only a few scenes from the original director, Kent Butterworth, remained). James L. Brooks is on record as calling the original version "s**t". As a result, the episode (which was originally intended as the series premiere) was pushed back as the season finale.
Anivision had worse animation than either AKOM or Rough Draft Studios; the DVD commentary mentioned that they had issues with keeping the characters' pupils the correct size (they weren't mentioned by name, but the staff pointed to "I Married Marge", which was animated by Anivision). Simpsons Archive also considers them the worst overseas studio, citing that they specialize in "lousy colors, misshapen figures (especially the eyes), and generally unfinished-looking, sloppy work."  They were let go by the end of Season 10 (either because of the quality of their work or because this was around the time Anivision was absorbed into Sunwoo Entertainment).
The FXX reruns of Seasons 1-20a are remastered and cropped from 4:3 to 16:9. Even though the colors are restored for the cel-animated episodes and the picture quality looks better, it looks really off-putting and claustrophobic compared to the original 4:3 aspect ratio.
Disney even used the 'remastered' 16:9 versions for Disney+, but they luckily fixed this issue by giving an option to view the series in the original 4:3 aspect ratio in May 2020 (not counting any of the episodes after the series switched to 16:9).
Unlike most Western and European shows being localized to Japan, it's Japanese dub lasted only 14 seasons, and after the movie was released in Japanese, starting in Season 15, the show is no longer dubbed by Japanese voice artists but is rather shown subtitled, an oddity for a foreign animated show in Japan.
It sometimes overuses pop-culture references, even in the earlier seasons. This also means that a lot of these references will go over the heads of younger viewers, as the Simpsons have always been intended as a more family oriented show compared, say, to the crassness of South Park.
Sadly, the series started to gradually go downhill since Season 11. However, Season 32 has shown to be a slight improvement.
"The Old Man and the Lisa" (Depending on your view)
Some of the couch gags (whilst very enjoyable) can get pretty weird or outright disturbing to some viewers (the "Treehouse of Horror" ones being notable examples).
"Stark Raving Dad" was banned after allegations against guest star Michael Jackson resurfaced in 2019 with the release of Leaving Neverland. It's bad enough to ban the episode from airing on TV, but to make matters worse, said episode was also removed from digital distribution and future reprints of the Season 3 DVD set, and remained absent on Disney+. Thankfully, it was back on the air through FXX on October 9th, 2019 and it can be bought digitally through Amazon Prime in the UK, but even that wasn't enough.
Certain characters, like Lisa, Agnes Skinner, Miss Hoover, Sherri and Terri, Patty and Selma Bouvier, Helen Lovejoy, Jimbo Jones and Nelson Muntz can be unlikable and/or annoying at times.
To be fair, Lisa isn't too bad in the early seasons, but by around Season 6, she started to become a soapbox for whatever liberal viewpoints the creators want to push. And even in those early seasons, she behaves less like an actual child and more like a teenager or young adult, expressing knowledge that no kid her age (at least back then) would know or care about, such as when Texas became a state, what a revolver is, who Mel Brooks and William Shatner are, or that Monaco has a prince. Not to mention her feminist Thanksgiving centerpiece in "Bart vs. Thanksgiving".
The show is a spin-off of a successful series of shorts on The Tracey Ullman Show from 1987 to 1989.
The first episode ("Simpsons Roasting on an Open Fire") is a Christmas special.
"Some Enchanted Evening" was originally going to air as the first-ever episode of the show in September 1989, but due to delays with said episode during production, the episode's plot had to be rewritten and pushed back to the season finale. However, according to the original production order of Season 1, it still remains as the first episode with the production code as 7G01.