Broken Base: Either this is one of the better of the made-for-TV Muppet movies to come about in the 2000s, or this is a blemish on the Muppets' integrity. The majority of Muppet Freaks really love this movie, feeling it did a better job capturing the original dynamics of the characters and their interplay, as well as maintaining the same sense of mayhem and chaos the Muppets' humor is known for; however, a Vocal Minority of fans feel this movie has none of that, that the movie is dark,trite, tries too hard to make the Muppets seem relevant and edgy, and pushes the envelope way too far in how much adult humor the Muppets display.
As time goes by, a strange reversal or softening up of opinion seems to be occurring. Many who once praised it as brilliant and just what the franchise needed think it hasn't aged well, while those who initially rejected it completely have come to admire that it kept the characters going when they were very much in danger of being forgotten.
In the Moulin Scrooge sketch, the Satine parody is named "Saltine". When CinemaSins did "Everything Wrong With Moulin Rouge!", one of the sins given out was "the most beautiful courtesan in the world is one letter away from being named after a cracker."
Nausea Fuel/Nightmare Fuel: In the alternate reality, Rizzo has one of the worst fates; he's in Fear Factor as one of the challenges, where he's locked in a cage and the contestants have to eat him alive. And he didn't even know about it.
True Art Is Incomprehensible: In-universe. The original opening number for the Christmas show (directed by a French choreographer that Gonzo hired) was... decidedly un-Muppet-like. Case A: it had a Muppet throwing glass Christmas ornaments directly at the audience.