Plot hole: Scully's statement that she was 23 when she wrote her senior thesis in college throws off her timeline of college, med school, residency, FBI Academy, Quantico teaching assignment for two years, and X-Files assignment at 28. Her undergraduate degree in Physics should have been completed when she was 20 or 21 to allow at least 4 or 5 years for her medical training.
Deliberate mistake: When the unconscious, naked Asian doctor is removed from the warming tub, his hands are clasped over his crotch to protect his modesty, despite the fact that he shouldn't be able to do that, since he isn't conscious and his previously frozen limbs are now pliable and relaxed due to the heat.
Continuity mistake: While Mulder's waiting for Langly and Frohike to unlock the exit door, Gray-Haired Man keeps shooting at the glass door, and the increasing bullet damage on the glass doesn't stay consistent as more damage occurs, and changes between the closeups and wideshots.
Add timeSuper Grover
Factual error: In the background the full moon is visible and it's early morning (approx. 6:00 AM). However, at the start of the episode we see the full moon at night (approx. 19:50). Due to the fact that these are consecutive days, this situation is impossible from an astronomic point of view.
Factual error: The last number on the truck's license plate is "77." On Russian plates the last two/three digits stand for a registration place. "77" is a number for Moscow, but the Gulag is located in Krasnoyarsk region, so the number should be different. Besides, the format of the plate (LDDDDL|DD) is incorrect - the correct one is LDDDLL|DD (L - letter, D - digit).
Plot hole: Eddie's ability to shape-shift is attributed to every muscle in his body being striated. While that's a reasonable explanation as to how he can change his face, it doesn't explain how he is able to change his hair. He has short hair and is balding, but when he mimics Mulder, he is able to match Mulder's longer and thicker full head of hair.
Add timeSerious B
Factual error: When Scully is performing the autopsy on Leonard Betts' severed head, she states "As remains are incomplete, all observations refer to a decapitated head." This phrasing is redundant. The proper terminology would be "disembodied head." As a medical doctor, Scully should know this.
Add timeSerious B
Factual error: The first time we see Ed's tattoo, it is supposed to have been freshly done and he even removes the new bandage. However, there is no blood or excess ink on his arm, no redness around the lines, no swelling at all; no way at all that it could be a fresh tattoo.
Continuity mistake: When Scully is searching through the pictures to find Sarah Kavanaugh and Sullivan Biddle, she turns the photographs over and they have a label on them to say who they are. Yet when the shot changes angle to show the photos from the back, the labels have disappeared.
Deliberate mistake: When Mulder is about to go into the metal detector he puts his gun on the counter. He goes through the metal detector on his cell phone but his keys set it off, when he steps through again it doesn't go off. No cell phones can go through metal detectors without setting it off.