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.
Revealing mistake: When the doctor examine Ronnie's "corpse" in the morgue, he pulls out the stake. It is quite obvious that he's struggling with a wooden stake that is placed on the actor's side, not through his chest. Moreover, the camera pans up and you can briefly see Ronnie's unharmed chest.
Continuity mistake: This is probably one of the most intriguing chess plays in the history of mankind. In the first move shown on the screen Gibson moves a white knight from e4 to f6. Then, in the close-up, the situation on the chessboard more or less corresponds to the arrangement of the figures previously shown on the screen. However, in the next shot, when we see the chessboard from the Russian perspective, the arrangement is completely different. Especially, there is no white knight on the chessboard at all. In the following shot the white rook suddenly appears on g8 (and is subsequently beaten by the black king), but in the next move Gibson again moves his white rook on g8, while the black king has miraculously returned to h8 and again beats the white rook. Moreover, Gibson could not play two white rooks, because later on we see that there is still at least one white rook on the chessboard.
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.
Other mistake: When Mulder is on his knees in the cafeteria talking to the gunman, there are several shots where you can see the sides of his jacket hanging wide open because of his raised arms, which would make the gun on his belt easily visible to the gunman as he talks to him, but he somehow doesn't see it until he goes to take Mulder's phone.
Revealing mistake: It seems that in the first shot the doctor injects something into the vaccine vial rather than extracting from it since the syringe plunger is moving inwards instead of outwards. In the next shot one can see that the syringe is being filled with the vaccine, however the arrangement of doctor's fingers is suitable for injection, which strongly suggests that the scene is played backwards.