Okay, so The Muppets Take Manhattan is supposed to be a different continuity than The Muppet Show and other productions, right? And I've always noticed that this is the only one where they don't acknowledge being in a movie. But I just noticed some slight fourth-wall breaking.
It comes when Statler and Waldorf see that Manhattan Melodies is on Broadway. Statler says "So they've finally made it to Broadway". So are they aware of the Muppets? It's a different continuity so they wouldn't have seen The Muppet Show. Earlier when they see Kermit and Miss Piggy at Central Park they don't seem to know who they are (Statler refers to them as "a frog and a pig"). They aren't shown watching the Muppets' performance at the beginning of the film, though in the comic book adaptation they are (I wonder if they shot such a scene and cut it).
There's also some confusion on Manhattan Melodies. At the beginning Kermit refers to it as a senior variety show, but throughout the rest of the film it's referred to as a musical, presumably with a narrative (though we don't see much narrative aside from "somebody getting married"). I assume that the performance at the beginning is meant to be Manhattan Melodies. I think it's on the sign at the beginning, and afterwards the Muppets remark that "they like/love it", as if they were pleaseantly surprised.
And throughout the movie, Kermit describes the plot as "two leads get married and then there's an opening number" which is "Right Where I Belong". But they sing "Right Where I Belong" before the wedding sequence, not right after (and if it came after it wouldn't be the opening number).
I don't know if the performance of the musical is meant to be the whole show or not (I saw an article last year on the subject, saying that the musical was rather short). Who knows how much more there would have been? But in the comic book adaptation they sing a little bit of "Together Again" after the wedding, which would make sense since they sing that song at the beginning of the film. It could be assumed that what we saw at first was the finale of Manhattan Melodies, but then we NEVER see Manhattan Melodies in full.