Bunsen makes a valid point that this film was actually the 7th (theatrical) film since The Muppet Movie, all but saying the Sequel Song was out of place. This seems right... until you realize that this film was the first to actually continue from where the last one left off, both as meta references and actual story events. That kind of continuity was unheard before 2011's The Muppets, and even that film used that continuity more as a tribute than as a direct sequel. No wonder this is the Muppet film doing a song about being a sequel; this is the first Muppet sequel.
'The Lemur' isn't actually that bad a name for an international jewel thief - modern meaning (and silly costume) aside, it's from a Latin word for 'ghost'.
It's also a fast, agile, clever little primates with a penchant for taking shiny things. Still no excuse for the costume.
The song "We're Making a Sequel" calls the movie "Muppets Again" which was the working title. However, they don't know the movie is about Constantine and the Lemur, so if they knew the movie was called "Muppets Most Wanted" then they'd know the plot.
Of course Animal could tell Kermit and Constantine apart: he could distinguish the smells.
Why couldn't Kermit get the fake mole off? He's made of felt. His hands are floppy and he has no fingernails. Yes, the mole was glued on, but even if it were just weak white craft glue, he'd have trouble.
A possible Brick Joke: Fozzie asks Kermit whether anyone reads the credits during the opening of The Great Muppet Caper, to which Kermit replies "Sure, they all have families." The credits to this movie end with Fozzie telling his mom she can go home now.
Why pay off reviewers and audiences just to keep up a farce with the Muppets just to steal the crown jewels? Could they be worth that much? Naw. It's clear from the start that it's not about any money that could be made. The villains just want to go down in history for stealing them, so they don't care about the price.
Perhaps more like Fridge Tear Jerker: the first movie was chiefly concerned about how the Muppets felt they weren't relevant and that no one cared about them anymore. Here they launch a comeback world tour that seems successful...until it's revealed that Dominic paid all of their "audiences" to come see their shows as well as newspapers to post rave reviews so as to keep the tour going and thus get to the museums he and Constantine were trying to get at. It's not suggested that anyone would have come see them otherwise. In addition, there's this throwaway line in the beginning of the movie:
Fozzie: "We're together again, and all our fans are back!"
Rowlf: "Actually, those were extras."
Fozzie: "I saw a few tapping their toes."
Scooter: "Yeah, those were paid dancers."
Well, that's why Kermit wanted to start small and work their way back up in the first place.
So, what's stopping Constantine from breaking out of the gulag and stealing Kermit's identity again? If the Muppets were stupid enough to fall for it once, surely they'll fall for it again.
Did Sam get his CIA job between movies, or is his Fox News parody opinion program from the first movie some kind of Federal program?
No, no - remember the opening scene. He was a Federal agent and always has been! It's just that before being sent to track down the Lemur he was undercover, in the role of an actor playing the part of 'Sam the Eagle' in The Muppets!