Visible crew/equipment: After the ship's captain delivers the Falcon to Sam Spade's office, he collapses on the leather sofa in the foreground. Just after Spade's secretary says, "Is he ...?", the shadow of someone's head passes over the sofa.
Other mistake: Detectives Dundy and Polhaus visit Bogart at 3:40 in the middle of the night as we see the time on his alarm clock after they walk in. In the previous shot it's impossible to tell what time it is time because there are no hands on the clock.