When Jeremy reaches through the tube to the interior of the car, he pulls back his hand with two knuckles scraped raw and a cigarette lighter burn on his hand. The knuckle wounds remain but the cigarette lighter burn disappears within seconds.
The White House postcard appears to be crooked and bent when Jeremy reads it for the second time, but it's in perfect condition when the box is filled up with liquid.
During the first 30 minutes of the movie, drops of sweat disappear and reappear on Jeremy's face.
With short wave radios, the person speaking must press a button to engage the microphone to broadcast, and cannot receive signal while the button is depressed. In other words, only one person can speak at a time. This is why people say "over" when they have finished speaking-- to indicate that they have finished taking their turn. It is not possible to interrupt someone while they are broadcasting, as is depicted in the movie several times.