First of all, any Catholic church presided over by a bishop is by definition a cathedral, not a church; secondly, Catholic churches and cathedrals are invariably named after a patron saint.
The shot at 6m 35s purports to show "Christ's Church Washington DC." There is a church by that name in the city, but it is not this one shown.
The agents are on a movie set during production, then the caption "16 months later" is displayed and they are shown at the movie's premiere. Afterwards, they are on the same set again for a final conversation. A production company would never keep a set around that long, especially after the movie is completed.
Gillian Anderson's stunt double can be seen after Tea Leoni asks Scully to show her how to run with high heels. It's also noticeable how the stunt double starts running before Anderson leaves the frame.
When Scully is alone performing the autopsy on Micah Hoffman, a shadow can be seen on the wall behind her. As the scene ends with her staring at her cut finger a person's shadow cross the wall behind her from left to right.
When Mulder and Scully are discussing zombies, Scully explains to Mulder that zombies and the like are just figments of the imagination. However in Millennium (1999), Scully encounters a zombie. She shoots at and is attacked by the zombie. She even reports such to A.D. Skinner. It seems unrealistic that an FBI agent would forget a past experience that was so unsettling.