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.)