Danny Trejo's mother passed away as he was filming his last scenes in this movie. As he was finishing his scenes so he could fly back to Los Angeles, California for the funeral, the cast and crew offered their condolences and sympathies to him. Trejo, known for his tough guy roles and demeanor, shrugged off the sympathies. When Steve Whitmire offered his condolences in character as Kermit the Frog, Trejo broke down crying.
Writer and director James Bobin ensured the special effects in this movie 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 The Muppets are the last bastion of it."
A lot of work went into making Constantine the Frog look slightly different than Kermit: 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. Constantine's puppeteer Matt Vogel swung Constantine when walking, giving the illusion of a heavy-shouldered man's swagger.
At the end of the "Sequel" song, Walter suggests calling the movie "Muppets Again". "Muppets... Again!" was the working title all through filming, but was changed at the last minute to "Muppets Most Wanted".
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 (2011). 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.
Ricky Gervais, Danny Trejo: appeared in this movie after having had their cameos cut from The Muppets (2011).
Christoph Waltz: 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, so he appeared as the guest of "Die Muppet Show" instead.
Steve Whitmire: Gulag prisoner carrying Kermit the Frog was also his voice actor and puppeteer. Notably, he keeps his head down in order to properly voice Kermit without giving himself away.