Continuity mistake: The dates on the academic discipline and progress forms for Max are not in accord with the order of the episode, coming after the "Millennium" episode. Supposedly the changes in his behavior and grades started a few months before, but the reports are from a few years ago. (00:24:55)
Continuity mistake: After Mulder has been released from the containment cell, and he and Scully go back to his room, the items on the table change position in between shots. (00:15:00)
Plot hole: The ability of the Faceless Rebels to impersonate other people completely defies logic. For one, when impersonating someone, the Faceless Rebel is able to speak despite the fact that they mutilate their own mouths shut. Secondly, as can be seen in many instances when a person is being attacked by a Faceless Rebel, the face of the person they are impersonating is merely a skin mask that can easily be pulled off. If the face of the person they are impersonating is just a mask, then any time a Faceless Rebel speaks you should be able to see their true face through the open mouth of the skin mask. Additionally, the face of the person being impersonated being a mask would also preclude the Faceless Rebel from blinking or moving the mask's eyes (similarly they mutilate their own eyes shut, so the eyes of the skin mask can't be their own).
Character mistake: When Mulder and Scully are in the graveyard, the headstone says "Howard Patrick Graves", but the newspaper said his middle name was Thomas.
Continuity mistake: When Dr. Kendrick/Eve is talking to the two little girls and she's clearing up the mess on the table, the position of the straw changes between shots. (00:29:55)
Kitsunegari - S5-E8
Continuity mistake: How was Modell tried and convicted in 1996 if he only woke up six months ago? Six months before this episode would be at least mid 1997. (00:06:05)
Field Trip - S6-E21
Continuity mistake: At Mulder's 'funeral' around when there is a knock at the door, we see Frohike raise his bottle to take a swig. The shot cuts to facing Scully and we can see Frohike further in the background and his bottle is nowhere to be seen, when he should've been mid-swig.
Visible crew/equipment: While Fox is fighting the agent in the underground garage you see a crew person on the right side of screen for a split second. (00:38:55)
Continuity mistake: General Callahan tells Mulder that the man he saw in his office said his name, but all he said was, "Your time has come, killer". (00:13:10 - 00:17:25)
Other mistake: When Mulder opens the body bag containing the "partial" remains of Max Pfennig (AKA Paul Gidney) a pulse can be seen beating in the right side of the corpse's neck. (00:18:10)
Continuity mistake: When Senator Richard Matheson tells Mulder about the four Japanese Nationals had been murdered, he says that the murders had occurred several weeks ago. But when Mulder brings Scully up to speed a scene or two later, he tells her that someone must have been able to identify the four doctors who were performing the autopsy because they were murdered YESTERDAY. (00:30:05 - 00:33:10)
Factual error: The date stamp says that it is April 12 and Scully says that it is Sunday, but April 12, 1997 was a Saturday. (00:03:10)
Sanguinarium - S4-E6
Revealing mistake: When Mulder and Scully enter the doctor's house, you can see over their shoulders that it is showering with rain outside, yet both of them are bone dry.
Factual error: The townspeople contracted Creutzfeldt-Jakob disease (CJD) from the bodies they consumed and it showed up in the brain tissue within a matter of weeks. However, this extremely rare disease takes several years to even be detectable. (00:18:55)
Kill Switch - S5-E11
Continuity mistake: In the same season episode "Unusual Supects" Fox Mulder's file lists him as Fox William Mulder. The A.I. discovers a similar file but the name is just Fox Mulder.
Continuity mistake: General Callahan, who is referred to as General Callahan throughout the episode by Mulder, gets called "Lieutenant" Callahan in the last scenes in the steam-room, while lying on the floor.
Anasazi (1) - S2-E25
Visible crew/equipment: As Scully stands up to leave at the offices of the Navajo Nation, the reflection of a boom mike moving in one of the picture frames on the wall can be seen. (00:19:40)
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