Other mistake: At the beginning of the episode, as B'Elanna is working her way out through the doors, the Doctor cowers and tries to hide behind things. There is no reason for him to be afraid. He can't be hurt under normal conditions - this proves to be the case later when he feels pain and says he is not programmed to feel pain, and we learned earlier in "Phage" that he can change whether or not things pass through him.
Plot hole: In the beginning, when the doctor is activated, he immediately asks who activated him. The computer tells him he was activated when a red alert was initiated. But then he finds out no one is on board, so there was no one to initiate the red alert at that moment. He should have been activated much earlier, when the crew was still on board and under red alert, even in a simulation.