The clock in the control room is always on twelve o'clock.
The satellite in space is visible on the screen in the control room. This would be impossible unless there was another satellite with a camera nearby.
When Doug enters the next room In Arthur Norton's apartment (13:10), he passes his hand over the light switch and the room lights turn on. However, the light switch remains in the "up" position the entire time.
Using footage of a Saturn V rocket to launch a relatively small satellite was a careless mistake. Certainly there were many more recordings available than the cinematic overused clip of the Apollo vehicle used to send 3 men to the moon.
The computer card that Barney placed into the back of the computer tape drive contained nothing but simple electronic parts such as resistors and capacitors. Even considering the computer technology of the 1970s being simple, a computer board without integrated circuits would be incapable of processing instructions.