Continuity mistake: A move is repeated in the opening chess game. The first overhead shot shows Gibson's white rook near the top left of the board. The adult opponent then takes it with his king at the bottom of the board. Gibson next moves the white rook to the bottom of the board and the adult captures it again, repeating his earlier move.
Continuity mistake: When the bank manager goes to open the door for the brinks truck containing the robbers, the clock on the wall reads 9:45. When the robbers are taking him back to the vault, a couple of shots of the skull-masked robber shows the clock reading about 9:43.
Plot hole: Mulder is pulled from the escape hole previously dug by the hybrid aliens to escape the train car. When they pull him out they show alien bodies remaining in the hole. Mulder never revisits the train car despite knowing there's a high probability of finding hard evidence, in this case some actual bodies. There's no way Mulder would just assume there's no evidence remaining there and not go have a look for himself. Same goes for Cancerman who thought he had destroyed the evidence.
Plot hole: After Mulder storms from the cinema at the end, Scully finds him sitting in the messy, deserted graveyard movie set. However, since the movie was premiering, which happens months after filming is completed, it makes no sense that the set would appear as if it was finished with that same day or that week.
Factual error: When Suzanne Modeski retreats to the restroom with a pair of pliers to pull out her tooth, she is only gone for approximately 15 seconds before the gunmen follow her. For a petite woman to rip out a strong, healthy molar from her own mouth (which also had metal prongs underneath in her gum) would not take so little time, no matter how determined she was. It's also highly unlikely that the lack of anaesthetic would have allowed her to do so without making pained noises.
Plot hole: On the phone, Scully asks for the report on her sister to be sent to the San Diego F.B.I field office (since she is visiting her brother and his wife and so is not in Washington), but the package is sent to her brother's home. Even if 'Danny,' whom she asks for the file, decided to be helpful and send it directly to her, her brother's address is not likely to be the one in her personal file, plus she didn't mention that that's where she'd be staying.