Christoph WaltzChristoph Waltz has a cameo as himself in the Berlin theater show. Waltz was the original choice for Jean Pierre Napoleon, but had to drop out due to scheduling conflicts.
One of the few The Muppets movies where Kermit the Frog and Miss Piggy are together in the first scene. Kermit rarely shows up right away and Miss Piggy always later and never together. For example in Muppet Treasure Island she doesn't appear until an hour into the picture.
The gulag prisoner carrying Kermit the Frog is a cameo appearance of his voice actor, Steve WhitmireSteve Whitmire.
Paul ReubensPaul Reubens ("Pee Wee Herman") has a cameo on a bus entering to HBO Studios.
A lot of work went into making Constantine the Frog look slightly different than Kermit the Frog:
His frill is shorter and wider than Kermit's
His eye slits are more horizontal than Kermit's, making him look angrier
His mouth was constructed to look like a frown
and Constantine's puppeteer Matt VogelMatt Vogel would swing Constantine when walking, giving the illusion of a heavy-shouldered man's swagger.
In the song 'We're Doing a Sequel', Gonzo mentions that they're waiting for Tom HanksTom Hanks to make Toy Story 4, most likely as a joke. Interestingly enough, Toy Story 4 was announced later that year (2014) for a 2017 release date.
James BobinJames Bobin ensured the VFX in the film were practical as much as possible: "We never go down the road of having a full CGI character, which you could easily do. The joy of this movie is The Muppets exist. They're real; you can touch them. There are very few forms of entertainment in the contemporary world that exist like that, and Muppets are the last bastion of it."
At the end of the "Sequel" song, Walter suggests calling the movie "Muppets Again." "Muppets... Again!" was indeed the working title all through filming, but was changed at the last minute to Muppets Most Wanted.
During Miss Piggy's song "Something So Right," she imagines what her's and Kermit's children would look like. This gag was originally intended to be in The Muppets, but was deemed too complicated to explain to audiences at the time.
Despite Bunsen Honeydew's comment that this is actually their seventh sequel, tthis is the is the first movie in The Muppets franchise to make numerous references to (and establish continuity with) a previous Muppet movie, in this case The Muppets. All previous Muppet movies rebooted afresh for each outing, so that characters could be given new origin stories whenever convenient, and "meet each other for the first time" repeatedly.