Jim rolls a 1971 Dodge Coronet down a road and over the hill, but when it goes over the hill and explodes the car is a 1967 Ford Galaxie.
When Jim takes off down the gravel road after putting out the signs, the car kicks a lot of dust into the air. Moments later the guards drive by, and there is no dust in the air at all.
When Casey put on Leona's mask, her hair was tied up. Later, when she takes off the mask, it's revealed that she has her hair down.
The guard uniforms are clearly labeled "Federal Prison Guard", but the car chasing after Jim and the "Suspect of the Week" is labeled "San Roberto State Prison". If it is a state prison, then prison staff work for the "state" and not for the "Federal Government".
The FBI "wanted poster" used to identify Larry Edison (Bradford Dillman) to Jim Phelps during the tape scene must have had pieces cut and pasted from at least two other real wanted posters -- although the name "Larry Edison" is used at the top, the wanted poster refers to someone named "Arrington" and someone else named "Crowley" in other text at the bottom of the poster as if that text were about the person depicted. These posters were indeed used in previous episodes.
The hypodermic syringe that supposedly contains a sedative that Jim Phelps (Peter Graves) uses to keep Larry Edison (Bradford Dillman) unconscious for an extended period of time after they escape from the prison is clearly labeled "Live Virus Vaccine."
Neither of the keys in the "Hide a Key" are Dodge car keys.
When Mr. Edison fires a revolver at Mr. Phelps, the revolver contains blanks. This had been established earlier, but between the time that this was established, and the time when the revolver was fired, (when Ms. Casey was pointing the revolver at Mr. Edison), the tips of bullets could be seen within the revolver chambers. Blank rounds do not contain bullets, and Mr. Edison only checked the revolver during the firefight where he used the revolver.
The chessboard is oriented incorrectly. The white square should be on the players' right corner.