I quite often start my car with the door open
Filming inside a car has to be one of the hardest shots without stabilisation. To get smooth shots you need suction mounts (for moving shots) and cranes (for static shots unless it's on wheels, with an engine).
That aside, nice work. My only comments would be from a style point you could edit a bit tighter to the music. That is to say the music could have been anything...