Deep Throat - S1-E2
Continuity mistake: When Scully is holding the guy's airbase security ID badge it changes between shots.
Plot hole: The bugs are related to a type of mite, and when they are shown under a microscope they look like a glowing lice without wings. The problem is they are swarming in the air so they have to be able to fly - no way to do that without wings.
Factual error: When Byers asks Langly to try under active cases to find Holly Modeski in the FBI database, Langly only presses two or three keys on a keyboard, which is obviously not enough to enter "Holly Modesky" to the search engine. (00:19:40)
Factual error: When two unidentified men who approached Susanne Modeski in the warehouse take out their handguns, they have regular pistols. However, when they start to shoot, continuous fire is heard that could only be produced by an automatic weapon. (00:28:40)
Suggested correction: Fully automatic pistols exist, such as the Glock 18.
Continuity mistake: The glass in the picture of Ryan Reynolds cracks as the casket is starting to catch fire. In one shot, which is wider, the glass has fixed itself. Cut to a closeup, the glass is broken again.
Revelations - S3-E11
Visible crew/equipment: The camera and its operator are visible in a piece of metal on the back of the ambulance, when the mother is taken away after the accident.
Nothing Important Happened Today II (2) - S9-E2
Factual error: Deputy Director Alvin Kersh tells Agent Doggett a story about King George III, who, on July 4th, 1776, the same day the American colonies declared their independence, allegedly made an entry in his diary: "Nothing important happened today." However, according to Arnold Hunt, curator at the British Library, King George III never kept a diary. (00:37:15)
Plot hole: Josh Exley's 'real' face shouldn't be visible as a reflection on the window. It's not an illusion that he creates to fool people, whereby his real self could theoretically be seen in a reflective surface, but a complete physical change, as we've seen in many episodes of the X-files regarding the shape-changing abilities of the aliens. What his face appears to be while altered is essentially what it is, and the reflection should show as much.
Other mistake: When Jerry Lamana goes up in the elevator in the Eurisko building, the "thirteen floor" message is missing. (00:20:55)
Continuity mistake: While Mulder and Scully are in the woods, in some shots it is raining, while in others there is no sign of the rain. (00:21:00 - 00:23:15)
Other mistake: Padget hands over one page of his book to his imagined character who is invisible to anyone else except him. Therefore, the page should hover in the air for an external observer. However, Scully watches his apartment on a monitor and notices nothing strange. (00:38:05)
Plot hole: Big Mike was attacked by the creature, because his bulb was broken just for a couple of seconds. It would mean that even if something like this happened to somebody else by accident, this person would also be killed by the creature. That would drastically increase the kill rate in the community. (00:16:15)
Suggested correction: That was the whole point of the creature, to enforce the HOA rules so that no violations occurred, even by accident. Although prior to the attack, Gene Gogolak describes Big Mike as a weak link that had to be dealt with, so the bulb was just an excuse to attack him.
Continuity mistake: At The Beginning of the scene in his office, in the front shot Skinner wipes his glasses in his hands, but in the following back shot he's wearing them. (00:12:25)
Character mistake: Pusher says that he read in Scully's files that she had shot Mulder, although after Pusher's visit in the Computer Records Office Skinner says that Pusher checked only Mulder's files. (00:40:15)
Factual error: When Mulder is walking out of the cabin in Spender's uniform, the soldiers try to stop him. This is impossible since he is an officer (a lieutenant judging from the shoulder-straps) and they are privates, so they cannot give him orders. The only thing they can do in this situation is to salute him. (00:08:40)
Revealing mistake: The establishing shot of Boston General Hospital at The End of the episode shows the same porte-cochère that was used for the BYU Medical Center in Provo, Utah eight episodes earlier in "Roadrunners." It appears they just digitally inserted this portion of the building over different facades. (00:40:00)
Suggested correction: These are two different porticos. The columns in the Boston picture show concentric grooves, and the fascia on the front of the roof structure is smooth and rounded. The Provo portico has smooth columns and the front fascia is composed of flat rectangular panels. In both pictures the porticos seem to be well-matched to the building structure and landscaping. It's unlikely that the production would have gone to the considerable expense (in the 1990's!) of a digital enhancement.
I could have worded the entry better, but while it's not the exact same portico, it appears to be the same building, but different entrances. The two structures have the exact same kind of writing on the right side and the overall design of the structures is remarkably similar, with some subtle differences in the columns and fascia, as you pointed out. Seems highly Improbable that a building in Boston and another in Utah that are not supposed to be affiliated with each other would look so alike.
It's also worth pointing out that the shot of the BYU Medical Center from Roadrunners showed the Kansas state flag flying outside the building, suggesting that the crew either had stock footage of the building, or they happened to be in Kansas and filmed the building in question. It's highly unlikely they went to the effort to find stock footage or actually went to a different building with a similar looking portico for the sole purpose of using it as an establishing shot of a different hospital in another episode.
After studying the photos again, I would have to agree that it is probably the same building, probably with an addition added to closely match the original construction. As to the improbability of two hospital architectures being so similar, I would reply that this may be common. I had occasion in the 90s to visit a hospital in East Lansing Michigan and later one in Alexandria Virginia that were virtually identical and owned by different health care systems.
Revealing mistake: In the opening sequence, a man who is hallucinating badly is apprehended by the police. They find a dead blonde woman in the trunk of the man's car. In a close-up of the dead woman, all the dried blood on her face is an added digital effect; however, the dried blood "drifts" around, seemingly out-of-sync with the video. Similar "drifting" digital effect problems are seen in other X-Files episodes.
Revealing mistake: As Dana Scully is examining the dead woman found in bed with Skinner, she observes a strange luminescent glow on the woman's nose and lips. It's apparent that this glow was added digitally; but the digital effect is "drifting" around the dead woman's face, seemingly out of sync with the video. Similar "drifting" digital effect problems are seen in other X-Files episodes.
Musings of a Cigarette-Smoking Man - S4-E7
Factual error: In the US classified information system there is "compartmented information", but there's no "compartmentalised information." (00:08:00)
The Sixth Extinction (2) - S7-E1
Factual error: When Skinner is at Kritschgau's apartment building, the time stamp onscreen says it's 5:05 AM, but when Kritschgau answers his door, he says it's 6:00 in the morning. Plus it is shown to be broad daylight outside. The sun is never up that early in Washington, D.C. (00:15:55)
