The scene of the red sports car with the damaged door is a stock clip used previously, to establish the fact the characters are at the police station.
There is no reason for Angel to distract the hospital front desk guy because Jim didn't use the distraction. It's just a plot device for Angel to recognize the patient.
When Angel pulls up in the 1959 Cadillac convertible, he tells the man at the hospital that is has a "special stick shift" in it. That big Caddy would have had an automatic transmission.
It is also probably far too heavy (about 5,000 pounds) for one person to push it so easily.
It is also probably far too heavy (about 5,000 pounds) for one person to push it so easily.