When John Colicos takes a German's weapon during the air attack, it is an MP40. When he uses the weapon to shoot the German shooting at the plane, it becomes an American M1 Thompson.
A German half track leading trucks carrying British prisoners across the desert breaks away to investigate another half track moving out of control. As it gets near there's a shot of the second truck running parallel to a set of fresh tracks seemingly indicating that this was a second take of the shot.
When the British fighter attacked the convoy the truck pulling the water trailer was hit and exploded. The water trailer was also engulfed in flames. The next day when the convoy pulls out they leave behind the blackened hulk of the burned out truck, but the water trailer is nowhere to be seen. All remaining trucks can be seen driving off led by the command car but none of them are towing a trailer.
When the tank overturns in the fuel depot, a turret hatch is clearly visible as open. However, Richard Burton's character has to force open a jammed hatch in the turret.
Burton and his group arrive on the clifftop above the big guns. As they're preparing for their assault a German force arrives and a fight takes place. At least a couple of shots of the Germans shows oil drums amongst their vehicles as if they were camped there.
Captain Foster fires more than the maximum magazine load of 8 shots from his Walther P38 pistol when he kills Captain Schroeder.
The Jerrycans on the German trucks just before the air attack were the American version with screw-on lids. The Germans would have used their own original versions which have clamped-on lids.
In the battle on the hill over the guns at Tobruk, Captain Foster (Burton) drops a mortar shell down a tube, pauses to give an order, then drops another shell into the tube. If you watch and listen there is neither the sound of a tube firing between the 2 shells being dropped into the tube, nor the visual puff from the end of the barrel which is fully visible during the entire sequence. Needless to say dropping a second round on top of a previously unfired one would ruin the gunners whole day.
The amphibious Grumman Goose isn't such an odd choice of aircraft considering it came from the port city of Tobruk.
German tanks displayed in the movie are actually M60s. The US M60 Main Battle Tank was first introduced only in 1960.