In many episodes, Jim closes the snap binding on the IMF folder, but when the camera zooms to it for the title sequence the snap is shown open.
In almost every episode someone has to pick a lock. They insert the pick, wiggle it a few times and open the door. To actually open a lock, the cylinder must also rotate just as a key would do. For this, a second "L"- or "Z"-shaped pick is used to exert pressure while the pins are moved with the first pick. This is never done.
In numerous episodes they load the villain's gun with blanks or give them a gun with some blanks and some real cartridges. Anyone who has ever fired a handgun would immediately notice the difference. Blanks make noise but have no recoil, real cartridges cause a recoil "kick" when fired.
In numerous episodes a very tiny black "tape player" is used. It is identifiable by the aluminum tape reels which each have three holes. This was a dummy prop and, in several shots, it is obvious that the tape is a continuous loop running around both reels since the shiny aluminum center of the "takeup" reel is visible rather than the brown tape color.
In multiple cases, Barney acts as a character such as a guard or an electrical worker in Eastern Europe. Since Eastern Europe had virtually no immigration from Africa during the 1960s, Barney's obvious African heritage would arouse immediate and very consequential suspicion.
In some episodes the tape recorder switch is shown on "rewind" instead of "play". (This is because the tape really is playing on rewind, the voiceover is edited-in afterwards).
Multiple episodes set in European countries have Barney working on electrical wiring to achieve the team's aim, yet the switchgear, outlets, and other equipment depicted is North American.
Cinnamon Carter is a famous model. (She is shown as "Model of the Year" on an "Elite" Magazine cover.) She would be recognizable worldwide, and could be a detriment to a secretive organization like the IMF.
Many of the photos that accompany the recorded instructions at the start of the mission look like they were taken by the same photographer (same background, lighting, and scale), even when the characters have no connection.
While the opening scenes of Briggs/Phelps playing the recorded messages are iconic, they are totally unnecessary. It would be far easier and more secure for an agent to simply deliver the top secret messages, rather than place them out in the public to be found by IMF, listened to in a phone booth, business, vehicle, etc., then dumped into an open vat of acid on a city sidewalk.
Delivery directly to the IMF leader would subject the delivery agent(s) to possible identification by any one surveilling the the location (or by members of the IMF team - clandestine operations try to minimize knowledge of people's identities even within the organization). It's presumed the person listening to the information has determined there is no one near enough to overhear; wearing an earphone to listen might draw more attention if someone were watching as opposed to being near enough to overhear.
Delivery directly to the IMF leader would subject the delivery agent(s) to possible identification by any one surveilling the the location (or by members of the IMF team - clandestine operations try to minimize knowledge of people's identities even within the organization). It's presumed the person listening to the information has determined there is no one near enough to overhear; wearing an earphone to listen might draw more attention if someone were watching as opposed to being near enough to overhear.
In numerous episodes one of the characters will unscrew an electrical outlet, then reach in and pull it out of the wall by grasping the sides of the outlet. This would put their fingers in direct contact with the wiring resulting in, at the very least, a severe shock.