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 you must also rotate the cylinder just as you do with a key. For this you would use a second "L" or "Z" shaped pick to exert pressure while you moved the pins with the first pick. This is never done.
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.
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.