Audio problem: When Jerry uses the elevator, the voice of the computer reads out the floors as "twenty-third floor, fourth floor, fifth floor" etc, missing out the "twenty-" prefix until the 29th floor. The DVD subtitles list these numbers with their prefix, so this was not intentional. (00:21:10)
Never Again - S4-E13
Visible crew/equipment: When Ed turns to go into the office, you see the reflection of the boom mike on the glass window. (00:05:30)
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.
Fresh Bones - S2-E15
Visible crew/equipment: When Mulder chases Chester on the pier, the camera's shadow can be seen as it circles around him. (00:25:25)
Continuity mistake: When Skinner walks into the cafe (the time he gets shot) another man is just walking out, leaving a table with a used glass and coffee cup. The waitress is in the back, getting Skinner a cup of coffee (she couldn't have cleaned the other table yet), but when we look over Skinner's shoulder you can see that the other table is cleared and has a clean coffee cup (turned upside down) on it.
Red Museum - S2-E10
Continuity mistake: When the old man shows Mulder the two guys, the one that is not Deep Throat's murderer, from a distant angle his shirt is completely red. In the close-up he has a red and a bit green shirt.

Continuity mistake: When the cup falls over when Lauren wants to see Mr. Dorlund, the box of tissues disappears in the last shot. (00:08:20)

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. (00:15:20 - 00:16:10)

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. (00:09:45)

Factual error: The flag in Skinner's office is hung upside-down. (00:28:00)
Visible crew/equipment: When Brad is showing Mulder and Scully the video tape in his house, you can see the crew reflected off the TV screen. (00:12:50)
Factual error: The Arecibo Radio Telescope is abandoned when Mulder goes there. However, after SETI was cancelled, the telescope was still used for other things. (00:16:50)

Other mistake: Mulder pulls in to park in front of a red car. The front plate on both Mulder's and the red car is the same: 5S2 706. (00:27:37)
Continuity mistake: During the conversation with Scully regarding Wayne Weinsider, Mulder says "I don't know why. I'm not a psychologist", which must be a big surprise for all viewers, to say the least. Mulder graduated from Oxford University with a Bachelor of Arts degree in Psychology (e.g. "Dreamland II") and he worked for some time as a profiler for the FBI (e.g. "Young at Heart"). (00:32:25)

Continuity mistake: In the close-up shot of Mulder just before he shoots Barnett, his black ear piece disappears. (00:42:15)
Continuity mistake: It seemed strange that Mulder was surprised not to find the Arthur Dales he knew at his apartment, when in "Agua Mala," he learned that Dales had moved to Florida. (00:08:30)
Answer: As he stated many times throughout the series, Mulder needed Scully to be sober and skeptical. Whenever Scully's skepticism wavered and she started questioning her own rationality, Mulder would try to restore her sense of skepticism, because he needed her to be clear-thinking.
Charles Austin Miller