Continuity mistake: When Mulder is in the Tram car ascending the Mountain, to rescue Scully, he pulls all of the things out of under the top left-hand seat, but when the scene moves to Krycek in the booth, you don't see any of the thing that Mulder threw out. (00:19:40 - 00:20:50)
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: After the meeting with Dr. Davey, we cut to Mulder sitting in the train station trying to figure out what Dr. Banton was doing in the video. We see an overhead shot of the station, which shows a column in the far distance. Watch carefully: the shot never loses sight of the column, and you can see random passersby walk towards the column, but NO Scully. As the camera moves downwards to focus on Mulder in the foreground, Scully suddenly appears from behind the column, as if she had been walking towards it all this while. Obviously, she had been standing behind the column until her cue to come out. (00:19:45)
Factual error: Mulder mentions the USS Eldridge as disappearing from Philadelphia (and later reappearing in Norfolk) "nine months after Roswell", i.e., May 1948. In fact, the supposed incident took place much earlier - in February 1943, according to almost all reliable sources. (00:06:50)