Wait a minute. So Gonzo ISN'T a famous British author?
Of course, this isn't something to be worried about too much. The original Warner Bros. animators re-told Bugs' childhood and his launch into stardom multiple times, as best suited them to tell a funny story. So this kind of thing is common practice. Having said that, attempting to make sense of the continuity is all part of the fun we have here.
So on with it.
First, regarding TMM. It's unthinkalbe not to consider TMM as much part of the canon as the backstage scenes at TMS. Yet TMM must be taken with a grain of salt, as some of the "history" doesn't quite line up with TMS (i.e. Scooter, etc.). It's like Kermit said: it's *approximately* how it happened. I think it's closer to the truth than any of the other movies.
In GMC, they announce right at the beginning that they're making a movie, so I've always considered it just that and nothing more (except of course for the "ad-lib").
TMTM is tricker because they are, in fact, entertainers, and they're using their own names. But good luck figuring out how that fits into the rest of Muppet history.
As for the wedding: yes, the joke was supposed to be that Gonzo was supposed to play the minister, but Piggy got a real minister instead. Thus, the debate has been fueled for years. In the seminal 1984 special "Henson's Place" (track down a copy if you haven't seen it already), Piggy tells the interviewer that they are in fact married, while Kermit insists, "It's all just a movie. We don't talk about these things." That's the closest thing we have to a definitive answer on the subject. I always took it that Kermit was telling the truth and Piggy was stretching it (look at similar instances in TMS). But since Kermit has always been reluctant to face his feelings about Piggy, especially in front of others, there is just enough of a margin of error to leave this open to debate.
Regarding the Muppet Babies: one would think they're part of the "alternate history" of the TMTM world. But in that world, Miss Piggy was merely dreaming. So then what was the 8 years of the animated series? Was Miss Piggy dreaming all that time? And what do we make of the live footage of the Babies in Muppet Family Christmas? To me, that special (one of the best things the Muppets ever did) is totally canon. So don't ask me to figure it out.
Christmas Carol and Treasure Island are both based on classic stories, and in both of them the characters actually change their names, so we can happily say they're playing parts in both (though Rizzo is just along "for the food" in MCC and so is pretty much himself).
MFS is the closest thing we have to canon in a Muppet film since TMM. However, the whole "Renfro" thing was obviously made up, so we have to take that with a grain of salt too.
Kermit's Swamp Years follows the continuity of TMM, so it can be pretty much assumed to be a mostly accurate prequel. Very Merry Muppet Christmas also followed the TMM continuity (i.e. the Doc Hopper reference) so, again, I would definitely consider it canon.
The backstage scenes of Jim Henson Hour and Muppets Tonight are also both canon.
Ironically, what I WOULDN'T consider canon are the talk show appearances. (No offense, Cory!) These are not well planned-out in advance or discussed in great detail with the writers, i.e. "Where are we taking the characters now?" Even if they have some idea what they're going to say, things can happen unexpectedly and the performers have to go with it, like the uproarious Today Show appearance in June '01 when Gonzo's eyelid got stuck in the "up" position and Dave had him saying all kinds of demented things as a result. Similarly, I wouldn't consider Kermit's "Porn's fine" comment as canon. I consider that as Steve getting flustered when talking about Snoop getting edited out of Very Merry and making a joke that he was probably embarrased about later. I'd consider TMM canon over that any day.
So those are my thoughts on it anyway. So just remember, Miss Piggy grew up in a nursery with Nanny, while Kermit grew up in a swamp, while Fozzie was a cub reporter, and Gonzo was a British author--from space.