Since 9/11 no pilot is allowed to be in the cockpit alone. If one pilot has to go to the bathroom or take a break a flight attendant takes their place to prevent this very situation, 1 pilot being able to crash a plane and no one in the rest of the plane can get in to stop them. FAA rules is that at least two people must be in the locked cockpit at all times during the flight.
It would not of been possible for the captain and the air marshal to break down the cockpit door with a food cart, or anything else on the plane including the air marshal's gun. After 9-11 all commercial cockpit doors have reinforced Kevlar within the panels to stop any hijacker from gaining access to the cockpit by shooting it. A passenger would not able to smash the door in as the doors also have reinforced titanium spars running the length and width of the door. Therefore if something was to make a strong impact against the door, it wouldn't cave in.
Chief Dodds calls Fin 'Detective' multiple times in the final scene. Fin has been a Sergeant for a while at this point.