The elevator at Sally's mother's building has the door open from the right on the ground floor but from the left on her mother's floor.
Stewart and Sally see Princess and go chasing off after her and the perp. When Princess is caught by the doorman, the McMillan's car has moved from the curb in front of the building to the curb on other side of the driveway. Neither Stewart nor Sally could have moved it because Stewart was chasing the perp and Sally the dog.
Stewart sticks his hand into the elevator to stop the door from closing but is unable to stop the door. Elevator doors are equipped with breaks. They prevent doors from closing in on and injuring people. They are easily triggered. Otherwise, elevators would kill people. Yet, Stewart struggles futilely to stop this elevator door from closing.
There was no reason for the motorcycle cop to pull Mac over for "speeding" on the bridge -- he was going no faster than several other cars around him.