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: When the invitation to the Hunt Ball is shown on the screen, it says that the ball is on Thursday, March 7, but on the night of the ball when Lena gets the telegram from Johnnie, the date of the telegram is March 8, 1938, which would have been the next day. And March 8, 1938, was actually a Tuesday and March 7, 1938 (the day of the Thursday Ball), was actually a Monday.