There would have been several layers of supervision between Mulder and Scully and Deputy Director Skinner, who would have been far too busy to personally supervise their section.
Throughout the series, in closeups of The Smoker's ashtray while he is extinguishing his cigarette, the filters of the "smoked" cigarettes already in the ashtrays are perfectly white, while they should be yellow/brown from the nicotine-smoke. This indicates that they are props, placed there before shooting and not cigarettes smoked by the characters.
Mulder and Scully are shown in numerous episodes carrying a variety of handguns from Glocks to Smith & Wesson to SIG Sauers. FBI agents are issued one model of weapon for standard duty carry and they carry those models unless they are lost, unless the agent changes assignments or the entire Bureau changes the brand and model it is using.
In numerous episodes in the earlier seasons, characters are seen driving cars with British Columbia License plates.
In many episodes it is clear that the agents are not in the region of the country or the world, described in the captions or the script. This especially becomes evident when the series began filming in Southern California and the vegetation and the terrain clearly could have only been that region.
Throughout the series, Agent Fox Mulder never has a camera with him in order to capture photographic evidence of the UFO encounters he has experienced and witnessed. These photographs could be included in his FBI case files to further prove the existence of UFOs.
Dana Scully wears high heels while running in many episodes.
In many episodes, Dana Scully is shown with long nails but wears latex gloves, her nails would go through the gloves, as they should be cut short.