Throughout the series when we see a closeup of CGB Spender's/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.
In numerous episodes in the earlier seasons, characters are seen driving cars with British Columbia License plates.
Muldaur 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 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.
There would have been several layers of supervision between Muldaur and Scully and Deputy Director Skinner, who would have been far too busy to personally supervise their section.