Other mistake: Twice in the episode it is explicitly said that Magnum's phone has been disconnected, and that Higgins checked with the phone company. Yet at the end, it turns out 'the lads' chewed on the cable. Surely the phone company wouldn't tell the estate manager that the line has been disconnected for billing problems (so, a well determined administrative issue with proper paperwork done) when it's a wiring problem.
Other mistake: Contrarily to what TC says, the alarm is not 'covered with corrosion', in fact it looks pristine. (00:16:55)
Other mistake: Magnum tells Higgins he has just twenty-three hours to solve the case when both the clock at the Nest and the one at the Honolulu Lulu's Pool Hall show it's half past four. Magnum though accepted Babs' case around 11:30 AM ("11:29 at the tone", Rick jokingly said). (00:07:35)
Other mistake: The license plate Magnum tells Rick to check out ("55 678") is totally different from the AYX 470 the guy was actually driving. (00:16:35)
Other mistake: The TV report about Magnum doing a Ready Player One backwards race, is shot from a perspective that would have required the cameraman to practically sit on Magnum's bike hitching a ride, in particular at the end. (00:48:25)