In Chapter: 9, the twin engine airplane changes into a single engine biplane during the parachute jump.
In Chapter 12, Grant tells Shirley to turn the plane to the right. Cut to an exterior shot of the plane--turning left.
In the final chapter, the reel of microfilm is actually a length of regular 35mm film. And contrary to Mr. M's claim that it's blank, images are clearly visible.
In episode 2, "Danger Downward" while pursuing the taxi driver, the cars pass down the same stretch of road several times.
In Chapter 4, "The Second Trap", the device placed on the bookshelf to eavesdrop has the ON/OFF switch set to OFF yet works fine.
In Chapter: 9, the train engine changes into a different train engine.