Other mistake: When Barton returns to his room to find one of the detectives reading out his film script, it ends with "We'll be hearing from that crazy wrestler, and I don't mean a postcard. Fade out. The end." When we earlier saw Barton typing the end of this script, enough was visible to show that the last line of dialogue was "We'll hear from that kid, and I don't mean a postcard", and there was no "Fade out".
Continuity mistake: After the scene where John Goodman kills the detectives in the hallway of the hotel, he is shown walking one direction down the hall to his room, then John Turturro is shown walking the other direction to the elevator. In neither of those shots is there a detective's body on the floor.