When Chance is watching himself on the large screen in the store window display, he uses his home remote control to try and change the channels on that set, but it controls another TV instead. However the remote is of the earlier "ultrasonic" technology, and these sound waves DO NOT pass through glass at the required strength needed to work. Those of us born before the movie can recall that jiggling your keys would make a remote controlled TV unwittingly change channels, or turn off and on. At about this same time the now common "infrared" RCs were coming out, albeit at outrageous prices. These signals CAN in effect pass through glass, despite some losses due to reflection. For the scene to be technically correct they should have used an IR remote, which would not make those "ringing bell" metallic sounds.
When the President is shown aboard Air Force One asking aids about "Chancey Gardner", immediately prior is shown a twin engine Boeing 737 taking off. A 737 has never been outfitted as a presidential plane. More accurately, a Boeing 707 taking off should have been shown.