Continuity mistake: When Jerry is on the bus with Alice, one second he's wearing his hat, he takes it off, then the next second it's back on, then it disappears for the rest of the scene.
Continuity mistake: In one scene when Jerry is entering the Federal Building, he starts through the metal detector, and he is stopped by a guard, and is asked for his keys, so he does not set off the alarm. Problem is, the guard, immediately hands the keys back to him, through the arch of the metal detector, yet it does not set off the alarm.
Continuity mistake: When Jerry is captured and strapped in a wheel chair, in his escape attempt he is rolling down a stair and the two footholds of the chair brake. Two seconds later, while the chair keeps rolling, the footholds break for the second time.
Continuity mistake: When Jerry first returns to his home he unlocks the fridge and takes out a container of food. Shortly afterwards he spoons some food into his mouth. He then puts the spoon back in his mouth with the bowl of the spoon inverted to lick it again. The camera immediately cuts to a different angle. He removes the spoon from his mouth but now the bowl of the spoon is the right way up.
Answer: Yes, that hospital may have had a trauma unit, but the NSA team, if they were NSA, led by Lowery / Hatcher (the guy who Alice 'knocked out') wanted to get Jerry away from Alice ASAP so that she would no longer be in any danger. The chopper then flew him, offscreen, to get patched up. Also we don't know that Jerry was airlifted to another hospital. But we can assume. An NSA controlled hospital. Or private government facility. A place where no questions would be asked.
Alan Keddie