Revealing mistake: In the last scene when O'Shaughnessy is being taken down in the elevator, one can tell that the elevator is not descending: rather something opaque is being lowered (like a window shade) to make appear as if it is descending. If you look closely through the translucent outer elevator door both the scissor-door pattern of the interior cab gate and the outline of O'Shaughnessy's torso remain stationary and don't descend.
Character mistake: When Spade leaves Brigid in her hotel room, he says he will buzz her buzzer long-short-long-short, so she will know it's him. When he does return, he only buzzes long-short.