Speaking about the "Fart Shoes" moment, I have a theory. It's simply my opinion, but here it is.
I think the reason the joke seemed very "un-muppety" is simply that they used the word "Fart". I think the shoes themselves are something that Fozzie WOULD use and I don't think it's a matter of intelligence. Fozzie was never stupid, but he was insecure and desperate for laughs. This isn't even the first time whoopee cushions have been used/mentioned. They were listed as one of their supplies in The Great Muppet Caper, and in The Muppets Celebrate Jim Henson they had the talking Whoopie Cushions. The "Fart Shoes" aren't all that different, except for the word "Fart".
To prove my point, think of Miss Piggy's "I've got to pee" line in Muppets From Space. Many fans, myself included, didn't like that line. On the other hand, no one had a problem with the scene in The Great Muppet Caper when all the Muppets were banging down the bathroom door, even though it was presumably for the same reason. The difference is that in TGMC, no one said "pee, poop, etc". We just had Animal yelling "BATHROOM" and Pops talking about people jumping up and down on one leg. Everyone knew what they were talking about, so they didn't need to use the more "vulgar" words.
I honestly think that if the Fozzie had said something like "Hey, Whoopie Cushion Feet" instead of "Hey, Fart Shoes", then not nearly as many fans would have had a problem with it.