Go to the part where Mia is driving to the ball in her mustang in the pouring rain. When she's lying in the car after the engine died, you can see the windshield wipers are still going. If the car was off, how could this happen? The windshield wipers are also on in her driveway, before you see her turn the key. I'm pretty sure this is a slip-up!
Yes, it is possible for the engine to die and the windshield wipers to still be on. It goes with the same idea that the radio can still be on if the engine is off. Its all about where you turn the key.
I agree that this is not a slip-up. When your engine dies, your radio and wipers don't turn off, and you can still roll automatic windows up and down.....not that her old mustang had them.