Continuity mistake: When Scully is in her room after the autopsy, we see the x-ray attached to her lamp. When we first see it, we can see the letters LD on it, yet when the shot changes back to the x-ray after Mulder has gone, we can only see I, presumably the other x-ray is now overlapping it.
Plot hole: Agent Spender watches in horror as Alex Krycek stabs the neck of an alien directly in front of him and the usual bubbling green blood spills out. In every other instance of a human being in such close proximity to the green blood, the person has immediately taken a painful reaction to the substance, including severe damage to the eyes. Spender however is completely unaffected, as is Krycek, who was also close enough to feel the effects.
Continuity mistake: When Mulder and Scully are driving after their plane lands, we see at one point that Mulder has his left hand on the wheel and he is eating a sunflower seed with his right, yet when the shot changes he's driving with his right hand and eating with his left.
Factual error: Mulder sees water going down the drain counterclockwise and says something is up since all water in the northern hemisphere drains clockwise. This is not true. Water can drain in both directions in both hemispheres. Things like convection currents, basin design, and residual swirl from filling the sink have a much greater influence. You would have to drain a small ocean to see the Coriolis effect, or use specially-designed test apparatus. See http://www.snopes.com/science/coriolis.htm and http://www.physics.ohio-state.edu/~dvandom/Edu/newcor.html (scroll down to *5.2. Water Going The Wrong Way Down The Sink* near the bottom of the page).
Continuity mistake: When Scully points out the location of the last time they saw Gibson Praise, she points to the (real) Palo Verde Nuclear Plant, which is west of Phoenix. In 'The Beginning' the plant shown was the (fictional) Rolling Hills Nuclear Plant, 60 miles east of Phoenix.
Continuity mistake: When they find the felled ancient tree, the stump that Mulder clambers up onto to investigate the growth rings has a distinctive crack at the center and the growth rings are irregular in shape. However the stump that we get a close up of has no crack and regular circular rings.