Mulders pistol switches between having sights and lacking them.
In the first scene after Mulder and the Red-Haired Man have been locked in the train car Mulder's Smith & Wesson 5906 pistol has iron sights. Next time we see them, it has none. Next time after that, it has sights again.
At 20:21 when the NSA agent first shows Mulder his key card, the stripe is on the right side, when it cuts back the stripe is on the left.
Scully draws a 9mm S&W on Agent X. At that time, the FBI special agents were carrying either Glock 23s (.40 S&W),Glock 20 (10mm) or SIG Sauers in 9mm. No S&Ws.
The journals in Dr. Zama's possession, handwritten all in Japanese, are seen a couple of times during the episode. On two different occasions, as Mulder flips through their pages, we can see that all of the pages are exact duplicates of each other: four identical pages in the original journal, and two identical pages in the "rewritten" journal seen towards the end of the episode.
When Mulder tells the conductor to leave them in a remote area, as the train is switching tracks you can see cars on a freeway in the background.
When Mulder flips through the book in Dr. Zama's stateroom, we see that the pages are all the same.
Between 19:00 and 19:15 there are two close-ups of what is presumably Mulder looking through the peep-hole for the train car. First shot is of someone with green eyes, second shot is with Mulder's hazel eyes.
In chapter 12 (at around 23 mins) the camera view changes to that from the television set. For no logical reason, this shot is flipped left to right compared to the reality the viewer has just been shown.
Mulder instructs the train conductor to stop the box car in the most remote place possible, but as the train pulls up you can see in the bottom left of the shot a red parasol and some equipment. This is not there when the train pulls away leaving the box car on its own in the middle of nowhere.
The final train chase happens in a mountainous area which is said to be in central Iowa. There are no mountains in Iowa.
Near the end of the episode, Mulder and Scully are discussing the events, and Scully makes mention of "Blue Earth, Iowa". The City of Blue Earth is located in Minnesota - there is no Blue Earth, Iowa.
The technician studying the implant chip that Scully had removed from her neck tells her that his tests on it "...destroyed its silicone matrix." Microchips are made of silicon, silicone is a silicon-based synthetic rubber.