Earlier scenes establish that the hotel gymnasium is below the lion statue, where the tape is. When Michael recovers the tape from the statue, a street is below him. When he falls, he ends up in the gymnasium.
Michael holds a glass in his left hand and grabs the champagne bottle from Dan with his right hand. When the camera cuts to another angle, the bottle and glass are in the opposite hands.
A chef takes a cake out of a hot oven without using oven mitts.
During "Hooray for Hollywood", some of the extras' lip-synching does not keep time with the vocals.
When Marlo and Dan leave the hotel gymnasium.