Factual error: When the audience are watching the pilot, Davy says "It's Russell!" But in the actual pilot, it's Micky who says it.
Factual error: When Mike punches the hole in the wall, he says to Harris that it could have been his face. In reality, he said that to Don Kirshner.
Factual error: As shown here, the Beatles really did throw a "welcome" party for the Monkees when they came to the UK. But unlike what is shown here, neither Mike nor Davy attended the event.
Continuity mistake: When Micky is talking to the guy outside the audition room, he has a red book and pencil with him. When he goes into the audition room, the book has disappeared.
Factual error: While this film does an excellent job of recreating the Monkees' overall "look," it gets their haircuts wrong. Davy only wore his hair in the long shown here for a bit of the first season (it's much shorter in the screen tests, pilot episode, and second season), and Micky didn't get his curly-perm, which he has in this movie from the start, until the TV series was in its second year. As well, Mike was known for disliking the wool hat and would not likely have worn it off-set, save for his audition and during the screen tests.
Factual error: In the record store scene, the Monkees' "Headquarters" album we see isn't the original release, but a 1980s Rhino Records reissue. The original release was on the Colgems label.
Factual error: Although the film (at least semi-) accurately recreates their outfits for the most part (notably in the episode and Head recreations, as well as at the Oscars), their costumes in the "Daydream Believer" sequence resemble their real-life all-white "Circle Sky" costumes, and look nothing like their actual "Daydream Believer." This sticks out due to the accuracy of their previous costumes, which makes one wonder if it was done intentionally.
Character mistake: After learning by telephone that he would be part of the Monkees and making records and a TV series, Mike says, "Man, it's a win-win situation." That expression was not in use in 1965; it didn't become widely used until the early 1980s.
Answer: He's in the wizard-looking costume as the suits walk into the studio sound stage.