In the tape message, the voice first correctly cites US scientists "Edward Stoner and Wilson Cardel" and their wives, but later refers to "The Wilsons and Cardels..."
After Jim crushes the light bulb in the flashlight (at around the 40:24 mark), the electrical wire that was pulled by "Ed" is clearly a single-strand wire. Jim says to "lead the wire back to the cell" but at the 41:41 mark, the wires are multi-stranded (it's very obvious, as it's a close-up, to show the spark).
Phelps takes the gunpowder from ten cartridges, wraps the powder in a handkerchief and uses it to blow a large hole in the wall. Gunpowder will not explode unless confined which it is not. Used as in the show it will only burn. Even if he could get it to explode the amount of powder he used would be insufficient to blow that large a hole in the wall.
The makeshift radio receiver Peter Graves was making up was built around a 6L6GC vacuum tube which is used as an audio output in guitar amps and high fidelity amplifiers. It requires somewhere around 300-400 volts to function and could not possibly work with a couple of flashlight batteries.
In reality the "San Francisco Gas Company" truck would be spotted as a phony. This areas gas service is P G & E (Pacific Gas and Electric).
When Rollin is doing the radio broadcast he says "This is KGO Fresno, CA". In reality KGO is a San Francisco AM radio station.
When Rollin inserts the first sonic probe the fake set wall clearly moves and flexes.
The chauffeur flinches in anticipation just before being struck from behind and knocked out.
During the faux earthquake, Cinnamon pulls a switch to cut the power in the adversaries hideout. But when Phelps is wiring up the makeshift radio, it appears that the overhead light in the room is illuminated.
To play the Voice On Tape message, Jim moves the tape recorder switch to the left, indicating reverse, but the tape moves forward.
When Cinnamon and Rollin and the guys who kidnapped them enter the lair, Cinnamon and Rollin have their heads covered with hoods so they can't see. We see the man who is holding them by arms say something to them, probably warning them that there are steps. His mouth moves, but there is no sound.