When Lina meets Don at the R.F. Simpson's party after the big premiere of The Royal Rascal, she mentions something like "I didn't see you last night at Wally Reid's party". Wallace Reid died in 1923 and the action of the film is set in 1927.
The film is set in the immediate aftermath of the release of The Jazz Singer (1927) with its industry-revolutionizing use of synchronized sound. However, dialogue dubbing of the sort central to the plot here was not possible until many years later.
When Lina is having problems talking into the microphone hidden in the bush and Rosco and the sound man are in the booth, the sound man shakes his head and says, "She's gotta talk into the mike, I can't pick it up." His mouth clearly isn't moving as he says this.
After the "Beautiful Girl" number, Mr. Simpson discusses hiring Kathy with Sid Phillips and Zelda Zanders. Sid Phillips delivers the line "Mr. Simpson might cast you as Zelda's sister." This is followed by an unusually prominent clicking mouth twitch, presumably out of character.
In the "Moses Supposes" scene, the book the Cosmo throws over his shoulder can clearly be seen to the left of the desk. By the end of the song, the book is gone and a miniature trash can has taken its place.
When Don and Kathy are in the car together there is no windshield, but when she pulls up to R.F. Simpson's house there is a windshield. And when she leaves his house the windshield is noticebly larger.
During "Make 'Em Laugh", the green couch slowly changes position. It is in front of the hallway backdrop when Cosmo first enters that part of the scene, but it has moved stage left by the time Cosmo does the back flip off the backdrop.
During the Cyd Charisse nightclub dance number when she's wrapped around Gene Kelly, her body completely changes position between frames due to a clumsy edit. According to commentary on the special edition DVD, this cut of only a few frames duration dates back to the original release of the film and no one knows why it exists.
When R.F. Simpson plays the first talking picture demo at the after party of "The Royal Rascal", the video is obviously edited in because as Mr. Simpson is walking off screen-right, the video cuts him off in a few frames.
The scene where Gene Kelly is shown performing in an action sequence from the silent film "The Dueling Cavalier" actually uses footage from his earlier film The Three Musketeers (1948). At one point, Lana Turner, who played Lady de Winter in that film, is briefly seen coming through a door to embrace Kelly before being immediately replaced by new footage of Jean Hagen hugging Kelly.
During "Beautiful Girls" number, the camera shows all the outfits curving downward starting with the pajamas and ending with the wedding dress. But when the camera closes in on the man singing and the women coming behind him, the wedding dress is in the middle with the others going outwards.
About three-quarters into the film Don Lockwood is with Kathy in the inside of a movie studio and showing her features of the background sky and showing her about lighting as he throws on the light switches. He comes to the area of the big fan and the blades are in a 10 o'clock and 2 o'clock position. As he returns to the fan the position is changed, and then changed back to the original position when he turns on the fan to blow on Kathy.
In "Make 'Em Laugh", when Cosmo sits down on the couch with the mannequin, his hat is pulled down over his forehead and the brim is flat. In the close-up, however, his hat is pushed back and the brim tilted up.
When the diction coach is reading 'Moses Supposes', O'Connor is making faces behind his back. When the coach catches him in the act, they both flinch. When the camera then cuts to a wider shot, you see them both clearly flinch again.
As the curtain opens on the preview showing of "The Dueling Cavalier", the title card shown on the screen spells it "Duelling". However, since both spellings are in fact correct (from a grammar perspective), it is entirely possible that one was used during production, and the other adopted only at the preview.
At the end when Kathy will sing "Singin' in the Rain" for Lina, Lina is asked "What key should the song be played in." She says "A-flat". The band leader says, "Singin' in the Rain in A-flat", and then proceeds to conduct the song in E-flat.