Lieutenant Schmidt is shown in Tarzan's house wearing a shirt and a bandage on his head. When he steps outside of the house, he now wears a jacket and the bandage is gone. He then walks over to a foot bridge, and the jacket disappears, and the bandage reappears on his head.
German paratroopers are shown in a plane getting ready to jump. They are all wearing helmets. The next shot switches to what appears to be actual wartime footage of a parachute jump, but none of the paratroopers in this shot are wearing helmets anymore.
When Tarzan is fighting the Nazis, he rips the magazine off a machine gun and tosses it to the ground. A moment later, one of the Nazis starts climbing to the top of the building to use the gun, and you can see the magazine still there. Yet when the Nazi arrives at the gun, the magazine is missing again.
Tarzan looks in the water and proclaims: "Cannibal fish!" All fish are cannibals: "cannibal" simply means "eats its own kind." The correct wording he should have used is: "man-eating fish!"
About 25 minutes in, when Cheetah jumps down a bed of leaves, as Boy cries out "Cheetah, come on now!" an obvious spotlight can be seen shined on the monkey.
As the German troupe treks through the jungle, they communicate with each other in perfect English.
Given Tarzan's prior hatred for guns, he should not have neglected to disarm the Nazi paratrooper of his sidearm pistol while the soldier was unconscious.