Other mistake: When Lady Penelope is relaxing with Jeff and the other members of International Rescue on Tracy Island, you can see in the lounge the pictures of the Tracy sons are in "Operation Cover-Up" mode, even though there are no other visitors on the island.
Character mistake: After the first Fireflash crash, search and rescue tasks are unable to find the wreckage, and John in Thunderbird 5 comments that its position was way off what was reported. However, he never bothers to relay this vital information to the London airport overseeing the rescue effort, and IR never bothers to attempt a rescue of a passenger jet filled with civilians, despite showing on the second crash that they were completely capable to saving them. It's then stated that the crash had no survivors, which the viewer has to lay at IR's feet. Even if they were busy with another rescue at the time, notifying the conventional rescue effort of Fireflash's real position could have saved many lives and given the investigation more evidence to find the problem.
Continuity mistake: After Thunderbird 1 is shot down in the Sahara, Scott is hanging unconscious out of the craft's front door. When Scott and Lindsey spot Thunderbird 1, the door to the craft is closed.