Other mistake: When Paul is assisting Nina with the underwater breathing apparatus, in Paul's close-ups we can see bits of tape along his neck hairline, for his hairpiece. (00:27:25)
Identified - S1-E1
Revealing mistake: When Sky One is launched, Peter replies, "Airborne, position 0-2-0 red," and in the following exterior close-up of Sky One, the four dark wires holding the aircraft are too obvious in this particular close-up. (00:31:10)