During the first truck scenes, it is clearly the middle of the night and the time is stated as 12:20 AM, except when the police cars pass the truck at 03:30, it is daylight.
When Fox and Scully gain access to the "power plant" they are trying to get to Level 6. The black guard who confronts them is a 1st Sgt in the US Army. In the military, 1st Sgt is an administrative position. They handle pay, discipline, punishment and grooming of the Company they lead. A 1st Sgt would not be guarding a door.
Not all sharks have to swim constantly to achieve a flow of water through their respiratory system, so not all sharks will die if they stop swimming; they must continue swimming, however, to avoid sinking to the bottom of the water column.
The polyester strips inserted into some US currency is neither metallic nor magnetic, and has absolutely no effect on metal detectors.
While following the truck, the electronics go haywire in the Taurus. When Scully slams on the brakes, the transmission shifter is in Park.
The 'bugging device' that Scully finds in the pen is just a collection of resistors, diodes and capacitors. It is fully rotated to reveal that there are no transistors which would be required to form a transmitter.
At the start, when we first see the agents in the woods, Scully is incorrectly using a camera with a telephoto lens to examine things very close up.
At 27:40 Mulder and Scully parked their gray car in front of a red car already parked on the street. Both cars have the same license plate: 5S2 706.
(at around 30 mins) When Scully is looking through binoculars in the car in the background, she (and her window) are clearly on a green screen because they contain interference.
When explaining the cover-up of the Roswell incident, Deep Throat mentions a secret conference between "the United States, the Soviet Union, the People's Republic of China, Britain..." in reality, the PRC was established in August 1949, more than two years after the Roswell incident, and therefore the Chinese Communist Party was unlikely to have been privy to such negotiations.
Frohike is using a SLR camera with a telephoto lens, yet it makes the shutter sound of a digital camera.
When Mulder and Scully wait for the truck on the side of the highway and drive off to follow it, the crew is briefly reflected on the car's windows.
(at around 29 mins) There is a large snow-capped mountain in the distance, even though Mulder is supposed to be driving through D.C. towards the Baltimore airport.
Mulder and Scully meet a group of UFO enthusiasts in a thick forest identified as being outside Mattawa, Washington. Mattawa is situated on a plateau in the high desert surrounded by sagebrush; there are no natural forests for more than 50 miles in any direction.