Stupidity: Staff Sergeant Duquesne is tossing and flipping rifle grenades before affixing them to his rifle to launch against the German tanks. A battle-hardened no-nonsense sergeant like Duquesne would never waste valuable time showing off, and would definitely not flip or toss around explosive ordnance like rifle grenades.
Stupidity: When Hugh O'Brian and the woman are on the beach, the Japanese planes shoot at them. Most unlikely that a plane would have gone out of formation to shoot at what appears to be a couple of civilians cavorting harmlessly on a beach, nor would the rear gunner have wasted his ammo on them.
Stupidity: Ilona Bergen's murder happening as shown is laughable; she sees the hand with the syringe coming, slowly, at her, and not only she can't defend herself or avoid it (because, damsels in distress in the 60s, you know), but she does not even scream. There's no way the killer could have been sure, or even take a calculated risk, to murder her in such a way. (00:55:25)