Other mistake: Magnum messes up his clothes at the gas station, all covered in oil, and uses them to clean the windshield. Still, when the snotty Brit girl arrives, he recovers them from the passenger seat. That would have royally messed up the interiors, and Higgins right there would have freaked out, but neither happens. (00:11:00)
Other mistake: At the appointment / trap at the abandoned shrine, Magnum hears a bell toll. He turn around, and it's clear that someone rang the bell pushing the log - it is still moving, it's not an automated system and there's no wind. but since the plot does not involve it, he just goes on like nothing happened. For all he knew, it could have been exactly where his supposed client or informant wanted him to go. (00:18:00)