(at around 55 mins) While searching through a chest containing many VHS tapes, Agent Scully's left hand quickly pans over the contents, revealing it to be without a latex glove; yet, in the next shot after calling over Agent Mulder, when she puts the video into the player, her hand is clearly gloved. She wouldn't have had time between the shots to put it on.
When Mulder and Scully enter Patnik's home, they hear a woman scream, draw their weapons, and search the house. They find two kids watching Die Hard (Bruce Willis) and it is implied that the scream came from the movie. The scene from Die Hard the kids are watching does not have a woman screaming in it.