Continuity mistake: In the prologue, the Nazis storm the Bresson residence. The elder Professor Bresson is sitting at his desk, back turned to them. There's an open fountain pen next to him, right by a paper sheet, but when Bresson answers rather defiantly to the bad guys, the paper sheet suddenly has disappeared. (00:02:15)
Continuity mistake: When Hodaka first fires his gun whilst being threatened by the man, the shell casing lands on the ground beside him, right next to his head. A couple seconds later, when Hina goes to help him up so they can run off together, the shell casing has vanished from the ground. (00:22:06)
Other mistake: Throughout this, a running gag is that Fred can't drive stick/clutch. However, in "What's New, Scooby-Doo?" Series 2, Episode 6 "A Scooby-Doo Halloween," he yells at Shaggy that he's riding the clutch too hard at the beginning of the episode. If the Mystery Machine has a clutch mechanism, he would know how to drive stick/clutch.