Factual error: On the night of the Hudson Building fire, the Auto Date Fixer in Commissioner Garfield's office reads 12/7/65. The next day, it reads 13/7/65, illustrating attention to detail on the part of the set decorator. Unfortunately, this overlooks the American convention for the month numeral to appear first. In the US the convention is month/day/year, in the UK the convention is day/month/year. So, either the first date should read 7/12/65 (July 12th) with the next day as 7/13/65, or the second date should read 12/8/65 (December 8th).
Plot hole: When Jeff Tracy contacts Lady Penelope, it is 10:00am in England, yet it is already daylight on Tracy Island in the South Pacific and Alan, Gordon and Tin-Tin have been out fishing for some time. (It is later established in the 1966 "spin off" movie "Thunderbirds Are Go" that there is a five hour time difference between Tracy Island and England. So, using that as a guide, when it's 10am in England, it should be 5am on Tracey Island.)
Revealing mistake: When the Plutonium store doors are blown off by the Jet-Air Blaster on the Laser Cutter Vehicle, you can see a length of string pulling the doors off from the inside.
Revealing mistake: In a close-up of the hitchhiker putting the bracelet on Prescott's wrist, you can see the bracelet is not locked on.
Visible crew/equipment: In a shot of the camera moving through the castle, the shadow of some studio equipment is moving down one of the pillars.
Continuity mistake: When the stranger waves at Prescott, telling him to slow down, we cut to Prescott in his car and you can see that the car has a windscreen, but when the car stops near the stranger in the next shot, the windscreen is missing.
Continuity mistake: When the laser vehicle leaves the pod and enters the plutonium store, you can see the cockpit has a windshield, but when Scott tells Virgil "We're gonna have to work fast", we cut to Virgil, and the windshield has disappeared.
Continuity mistake: While Prescott, Dempsey and Kenyon are in the castle, there is a glass, a bottle and another glass (in that order diagonally) in front of Prescott. In a close up shot of him, the green bottle has move several inches to the left.