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).
Factual error: In the scene where Mulder, the police officer and the doctor are in the doctor's room, the time on the clock reads 8:40. The doctor announces that he going to the bathroom. The scene cuts to him in the bathroom and then back to the doctor's office with Mulder and the police officer. Another cop comes in and says, "Come to the bathroom, something's happened." The clock still reads 8:40.
Factual error: After the agents meet with Kevin's father in the mental institute, Scully lists the medication that he is on: haloperidol, loxapine, and chlorpromazine make sense, but the fourth medication - LARGACTIL - is in error. Not only is it a brand-name of chlorpromazine, but it is not available in the USA, it is a CANADIAN drug. (00:36:10)
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)