Continuity mistake: When Stevie the little boy is in the cave, there are basically two shots: One from behind his three friends looking down, and one from Stevie's perspective, looking up. Every time we look down into the cave there is quite a lot of sand trickling down, but when we are with Stevie in the cave looking up, there's no sign of it.
Continuity mistake: When Mulder and Scully stop by the fence after chasing the tanker trucks in Texas, Mulder takes out a map, opens it then folds it and looks at it closely. The map looks folded differently in the two subsequent shots, then is shown wide open again in the third shot when Mulder starts folding it again.
Continuity mistake: When Mulder has Scully thrown over his shoulder and has to set her down to perform CPR when she stops breathing, her hair is pasted over the side of her face. Then, all of a sudden, the hair is gone. When Scully starts breathing again, Mulder smooths back her hair, and in the very next shot, the clump of hair is back.
Continuity mistake: At the beginning where Mulder and Scully are on the roof searching for the bomb, you can clearly see Scully gripping the door knob and she holds it. When Mulder tries to grab the same door knob, Scully gets out of the way and crosses her arms. The next thing you see is Scully with her arms uncrossed.