Many episodes will contain occasional uses of ass, crap, hell, damn, freakin', bastard, gay, and infrequent uses of bitch, slut, and whore. There's censored swearing in a Halloween episode where Maggie attacks a newsman and some other episodes,but this in not a regular occurrence and is ALWAYS censored.
Homer (the dad), Bart (the son), and Abe (the grandfather) are each the most often guilty parties of using curse words (minimal major words).
Bart Simpson frequently uses the catch phrase "eat my shorts" which may be interpreted in a sexual context, and was once in the episode "We're On The Road To D'ohwhere".
Apart from the deleted scenes on the DVD sets, the mild language isn't that harmful, some episodes don't even have a single swear.
The character of Ned Flanders may be considered as a mockery of Christianity. There are many jokes and mockeries of religious themes (mainly Christian, some Jewish, Buddhist and Hindu) that some may consider rude.
A few mild racial slurs. Frequent parodies of various cultures (somewhat offensive but still funny), including American, British, Irish, Scottish, French, Hispanic, Italian, Russian, Chinese, Japanese, Jewish and Australian. Ethnic and religious stereotypes are used and abused. They are not used in racist ways but rather sacrilegious ways.
In one scene in a season 12 episode, a character uncensored tells Marge to ''Shut the fuck up''. The scene was never televised, but appears on the season 12 DVD as a deleted scene.
Note that there is more profanity in modern Simpsons episodes. If one were to watch an episode from an earlier season, you'd occasionally hear "damn", "hell", and "bastard", but nothing much. Nowadays, there is harsher swearing, but it did die down in Season 24.