Fresh Bones - S2-E15
Revealing mistake: While Mulder, Scully, and the groundskeeper are walking through Folkstone Municipal Cemetery, there is a partially hidden but still conspicuous sign that reads "Vancouver Cemetery." (00:18:45)
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)
The Sixth Extinction (2) - S7-E1
Continuity mistake: Mulder writes Kritschgau's name on the ulnar side of the palm of Skinner's right hand. Later when Skinner is looking for Kritschgau in his apartment building, the writing is on a different part of Skinner's palm, beginning around the middle and extending diagonally towards the thumb. (00:11:50 - 00:15:30)
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.
Invocation - S8-E5
Continuity mistake: In this episode the character of Billy Underwood was played by twin brothers Kyle and Ryan Pepi. If you pay attention you can tell when one twin was being used instead of the other as one of them has two freckles on his neck and another two by his right eye whereas the other does not.
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.
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)
Continuity mistake: Just as Mulder and Scully are entering the interrogation room to question Lauren for the second time, Mulder is holding a thin stack of paper, folded in half in his right hand. In one shot, these are folded horizontally. In the immediate next shot, they are now folded vertically. (00:34:20)
Unrequited - S4-E16
Revealing mistake: The handle and latch next to the supposedly working intercom on the chain-link security gate entrance to the "White Hand" facility is obviously non-functioning - when the gate is opened it can be seen there are no functional operating parts. (00:08:40 - 00:09:15)
