Visible crew/equipment: I don't know if this is visible in all formats, but on the newest UK release on DVD, watching in widescreen, it's amazingly obvious. When Mulder recovers from the vampire attack, he gets up from the floor and breaks up a chair to make a stake. There is a shot of his feet as he smashes the legs off and bends to pick up a piece. In the bottom left hand corner of the screen, you can see a crew member's hand carefully and quickly placing a piece of wood on top of the pile for Mulder to pick up.
Visible crew/equipment: A mic boom operator is visible on the left hand side of the screen wearing a white t-shirt, beige shorts, and sneakers. He's carrying the boom mic and following Mulder and Scully. You can see him when Mulder and Scully arrive at the "Church of God with Signs and Wonders" for the first time...when Mulder delivers the line "That's funny, I knew a couple Catholic schoolgirls who were experts at it."
Revealing mistake: While the computer is being infected with the virus, Peterson turns away from the screen to face Scully. Two seconds later, after the shot of Scully, the same shot is shown again but in reverse so that Peterson turns back to the screen. It's more obvious if you look at the weird way his eyes blink in the reversed shot.
Plot hole: Scully's statement that she was 23 when she wrote her senior thesis in college throws off her timeline of college, med school, residency, FBI Academy, Quantico teaching assignment for two years, and X-Files assignment at 28. Her undergraduate degree in Physics should have been completed when she was 20 or 21 to allow at least 4 or 5 years for her medical training.
Continuity mistake: When Mulder experiences his near-death trance state his body is lying, apparently lifeless, in a star spangled sky. As the camera tracks in on him the toes on his right foot twitch, just after Deep Throat begins to speak. The foliage covering his chest also changes position between shots. In the wide shot he is covered up to the armpits. But the first close up shows his chest is exposed. Then in later close ups it is covered again.
Visible crew/equipment: When Mulder and Scully enter the abandoned mine through a doorway, the viewer can see at right in the distance a number of people sitting on a wall, and one crouching in front of the wall with what looks like a dog. They are sitting still, but there is still movement there.