The mission tape recorder is switched when the tape self destructs. Not only is there a different take up reel, the machine is dirtier and has holes drilled under the take up reel around the hub for the smoke to come out of.
The unit that Willy connects to the car to make it remote controllable is simply a Radio Shack Micronta code practice oscillator. This unit would have absolutely no radio control or remote operations capability.
The newspaper article about the "Motorcyclist Killed" is padded, after the first paragraph, with unrelated text, taken from another column on the same page.
When Pete and Susan enter his dressing room after the fight, you can briefly see the camera operator and camera in the mirror.