Visible crew/equipment: When Lionel returns to the jazz bar and discovers Billy Rose has been killed (framed as a suicide), you can see two people standing in the shadows to the left of Lionel as he enters the main room where the stage is located. A man is hunched over, whilst a woman is standing still wearing what looks like a dust mask. (01:32:27)
Factual error: Through the last third of the movie Edward Norton has a cut above his left eye. It is closed with an adhesive strip. It wasn't until 1962 that 3M™ Steri-Strip™ Skin Closures were introduced to the health care world. A stitch or two would have been less distracting, and would have been better suited to the gritty feel that the movie was trying to achieve.
Continuity mistake: Last scene, camera front, he's strolling her back. Next view from behind, she's strolling his back. The front view, he's still stroking her back.