Revealing mistake: When Thunderbird 3 lands in London, the jets do not burn the grass they land on.
Continuity mistake: When Alan, Vermont and TinTin are hanging upside down looking into the control room, TinTin's crystal is hanging around her neck, in the next shot it disappears then reappears in the 3rd shot.
Factual error: As the Hood approaches central London in Thunderbird 2, they fly through Tower Bridge and over HMS Belfast, approaching from the East. However the onboard display in Thunderbird 1 shows TB2 approaching from the West, somewhere over Hammersmith.
Factual error: About 2/3 of the way through the film, the Hood uses an electro-magnetic pulse device to disable the alarms in the Bank of England: the lights in the vault remain completely unaffected. This is rather tame; consider the widespread effects of the EMP devices deployed in 'Goldeneye' and 'Ocean's Eleven'.
Other mistake: Wouldn't Thunderbird 1 leave some sort of burn marks on the pool side as it lifts off? The blast pattern is close enough to the sides.
Continuity mistake: When Lady Penelope and Parker are fighting the bad guys in the Tracy island living room, it gets completely trashed, smashing glass, throwing sofas etc. Later, when they take off in Thunderbird 2, there is a shot of them flying past the house and the living room looks normal again. Surely the Hood wouldn't bother to tidy up after the fight?
Plot hole: Near the end of the film, the crippled Thunderbird 5 is about to catastrophically re-enter the Earth's atmosphere and burn up. Predictably, the younger Tracy brother restores control, saves Thunderbird 5 and all on board. A few seconds later, a computer announces that Thunderbird 5 has resumed a geostationary orbit (such orbits are only possible at an altitude of 400km) My point? Pulling out of a fall, climbing 370km in a few seconds, and then stopping dead 400km up would have required such a massive acceleration/deceleration that everyone on board would probably have been pulverized, even if it were possible for a badly-damaged space station to move that fast.
Revealing mistake: When the kids run away from the crooks on Tracey Island they roll down a hill into a lagoon or so. Look carefully and you can see the persons rolling down the hill are adult stand-ins.