In the traditional sitcom fashion it is usual that by the end of a given episode of The Simpsons, everything is back to the way it was at the start. This means that shows can be aired in pretty much any order without causing really huge contradictions. However this is not a hard and fast rule. In addition to the only ever two-part Simpsons episode - Who Shot Mr. Burns? parts one and two, which made up the season six finale and the season seven premiere - the following major events have had permanent effects on the structure of the Simpsons universe...
Combined in with these are various more minor events which characters frequently make references back to. Bart wishes he had an elephant, and Lisa reminds him of the time he owned Stampy; Homer shows off his Grammy award; Blinky, the three-eyed fish, reappears. Gravestones from dead characters turn up. These are some of the more overt references, but for the sharp-eyed viewer there are more subtle ones: barrels of Li'l Lisa's Patented Animal Slurry seen underwater; the head of the Olmec Indian god Xtapolapocetl frequently appears in OFF's basement; Homer's Mr. Plow jacket turns up in his closet along with numerous other old trinkets. The Simpsons has often been described as a show which rewards the viewer who pays attention.
However, these pleasant surprises for the observant are the exceptions that prove the rule. Disregarding the deliriously contradictory retconning of episodes such as (4F23) The Principal And The Pauper, the toughest continuity issue for the Simpsons fan is temporal continuity. What year is this? How can they have had EIGHT Christmas episodes* and yet Bart and Lisa are still 10 and 8 respectively? How can Manjula have conceived, been pregnant for nine months and given birth while Maggie has apparently not aged? Lisa was born during the 1984 Olympics, but she received her saxophone at the age of three in 1990? How can Homer have graduated from high school in 1974 and still be only in his late thirties? How have Homer and Marge been married for ten years for fifteen years? It goes on and on, to the point where any sane individual would give up. Which I did.
The Simpsons is perhaps best described as a single gigantic continuity error. The Simpsons Model of Temporal Continuity is as follows.
The last rule is probably the most important. Take each episode at face value, don't think about past continuity until the show tells you to, and just enjoy the ride.