Continuity mistake: When Scully is talking to Skinner in Mulder's empty hospital room, her cross necklace is off to the left. Then, when she says, "Sir." it's almost centered. And no, this was not caused by her turning around a minute or so before she said it.
Continuity mistake: When Mulder and Scully are driving after their plane lands, we see at one point that Mulder has his left hand on the wheel and he is eating a sunflower seed with his right, yet when the shot changes he's driving with his right hand and eating with his left.
Plot hole: When Mulder and Scully are going to the town/city where the disappearances took place Scully says they should stop so she can walk the dog. Mulder says OK because he has to ask for directions yet the next scene we see is Mulder and Scully interviewing Dr. Faraday. How did they find him if they didn't know where they were?. And after that we see them at a store where they do ask for directions.