Other mistake: In the scene where Mulder and Scully are first visiting Darlene Morris, there is a split-second shot of Mulder examining residue on his fingers that is edited in between Mulder and Scully ascending the steps to the porch and knocking on the door. It's as if the sequence was initially longer with Mulder discovering a suspicious substance before he and Scully knocked on the door that was not completely edited out.
Continuity mistake: When Frohike plays the slot machine, the first position on the reel shows a single bar. After Byers spots Suzanne, the camera goes back to Frohike and the first position now is not a single bar. There wouldn't have been enough time between the shots for Frohike to have another pull of the machine.
Continuity mistake: Mulder says that Scully was abducted and missing for four weeks. In "Duane Barry," the date stamp is given as August, then in "3," when Mulder returns to the X-Files office he turns the calendar all the way to November. Since Scully is returned the next episode after this, she must have been missing for at least 3 months, not 1.
Factual error: In the scene where Mulder, the police officer and the doctor are in the doctor's room, the time on the clock reads 8:40. The doctor announces that he going to the bathroom. The scene cuts to him in the bathroom and then back to the doctor's office with Mulder and the police officer. Another cop comes in and says, "Come to the bathroom, something's happened." The clock still reads 8:40.
Continuity mistake: After the meeting with Dr. Davey, we cut to Mulder sitting in the train station trying to figure out what Dr. Banton was doing in the video. We see an overhead shot of the station, which shows a column in the far distance. Watch carefully: the shot never loses sight of the column, and you can see random passersby walk towards the column, but NO Scully. As the camera moves downwards to focus on Mulder in the foreground, Scully suddenly appears from behind the column, as if she had been walking towards it all this while. Obviously, she had been standing behind the column until her cue to come out.