You have to take the batteries out of the clock when shooting otherwise some poor shmuck has to run and reset it for every shot. That interior scene had a lot going so it took at least several days to shoot. When it's such a long and complex scene, clock continuity is kind of the least of your worries.

As for the license plate, I think it may also just be a simple continuity error rather than some sort of intimation. There were quite a few locations where that car was used - definitely not shot in sequence - and because it's an operational car, there may have been some back and forth on changing the plate from a real one and a fake one. I don't know how they managed to screw it up - maybe someone got royally chewed out or maybe it just didn't matter so much - but I think a better focus would be on the conspicuous details rather than what could just be a continuity error. Especially if there were reshoots or simple b-roll stuff shot later or before, I could see the plates being misplaced or changed along the way. And because it would take awhile to get another license plate made to exactly match the previous one and you're on a schedule, they just changed it out and hoped for the best.

Point is, this show has such a wealth to dissect, I think it might be reaching to find meaning in continuity issues.