Now this is a topic that has always interested me. I'm feeling a bit under the weather now, so I might not make much sense, but I'll try.
Nah, continuity was never a big thing on OFF, at least not to the extent it was on Futurama. Still, there have been certain, how shall I put it, "trends" developing. (Mrs Krabappel's and Skinner's relationship, Milhouse's love for Lisa etc.) Then again, they've had all those Christmas specials and finished school thrice and whatnot. I think canon, too, is a rubber band. (Or maybe I just can't be bothered to make a definite statement.)
I agree with Sheana about the "prediction" episodes. That's what they are, predictions. They're forking prophecies, man! They're not necessarily the truth. "Lisa's Wedding" was aired before the episodes about Skinner and Krabappel falling in love, so of course, in it Mrs Krabappel was still an embittered old divorcee wanting to catch the bouquet at the wedding. So, both "Lisa's Wedding" and "Bart to the Future" may be far from the actual truth. (The fact that, IMHO, "Lisa's Wedding" rocked and "Bart to the Future" sucked is another story entirely.)
Utterly agree with Graham about intra-episodal continuity. This may be a cartoon, but there's no reason to make it *cartoonish*. (Such as Bart taking Homer's eye out.) Everything, of course, has to go back to normal after 22 minutes, but gee, not even Itchy&Scratchy brings Scratchy back from the dead in the same episode.
But, yes, this is a tricky issue. It's been a long time since I've written a Simpsons fanfic, but as I seem to recall, my own makeshift solution was to choose the bits of continuity I liked and ignore everything else. I mean, sometimes you have to do that, or you'll go mad trying to piece the threads together. Why aren't Bart and Lisa still at Rommelwood? OK... I have no answers to anything.
Going off-topic for a moment. Cover your eyes, kids.
Lisa's presidency: OK, this is personal. I'm a bit annoyed when people seem to think that referring to Lisa as the future President of the United States is the same as referencing "Bart to the Future" (which has been deemed to suck by me and many, many other fans). Lisa got morals. Lisa got brains. Electing Bill Clinton for office why not Lisa Simpson?
No, seriously, both "Lisa on Ice" and "Lisa the Iconoclast" showed the possibility that Lisa might become President one day. This possibility was presented in fanfiction by Graham, Jason and yours truly. And, well, we don't suck.
(Though it is my belief that since Lisa gave up ice-hockey and refused to tell the truth about Jebediah Springfield, she probably won't become President after all.)
Let's face it. I didn't laugh once during "Bart to the Future", though I winced several times. But it got something right.