While Jim is rescuing Miss Lawrence from drowning, Tamba the chimp is jumping around on shore. As Tamba is jumping around, Jim's hat is right next to him in long shots and nowhere near him in close-up shots.
While planting a dynamite charge in a river, Jungle Jim sees a nurse shark and an octopus, and then watches as the two do battle to the death. In reality, a river in the heart of Africa would be unlikely to have sharks, and certainly would not have octopus inhabiting the shallow, fresh waters.
In an early scene when Miss Lawrence first meets Jungle Jim after he saves her from drowning, she's admiring his features, and asks him to 'turn your head to the right', to which he turns his head left!