Plot hole: In one scene, he's driving from Los Angeles to Berkeley in a hurry, and crosses the bridge again (in the wrong direction). But the most direct route from L.A. to Berkeley doesn't require you to cross the Bay Bridge in EITHER direction.
Plot hole: When Mr. Bigger arrives at the hospital, he slides out of the trolley. Look carefully : he was not in the trolley.
Plot hole: When the Major and Wadislav walk up the stairs in the German mansion they are met by a pair of German officers who say something to them. Wadislav then tells the Major that he couldn't understand a word they said. What they actually said was 'Nice weather, wouldn't you agree?' Wouldn't you think that a man who speaks German well enough to convince the guards in a German HQ would understand such a simple phrase? Wadislav was chosen specifically for his ability to speak some German.