In the camping scene, Mona takes the coffee pot to the creek to get water. But it is still on the camp stove in the next scene.
Doc is taking a swim when the coroner arrives and exits the pool soaking wet. Moments later when the Five arrive poolside Doc is dry.
Fantasy elements aside, gold boils at close to 4,000 degrees. The gold pool could not exist and the tribe could not live in its proximity.
During the scene where Doc Savage and his comrades are pursuing the sniper, modern (1970s vintage) automobiles can be seen in one of the aerial shots. The film is set in 1936.
Outside the Broadway Ticket Agency, posters on the window are for films, not live shows, which were never sold at such agencies; one of them is for Tarzan and the Leopard Woman, which was released in 1946, not in 1936, the year in which this scene is supposedly taking place. Another is for Bohemian Girl, which would have been OK, except its for the 1946 re-release, and pictures a generic image of Laurel & Hardy, as they often appeared in their other films, but not in this particular one.
After the attempted shooting of Doc and his men in the penthouse apartment, Johnny remarks that the "refractive glass" windows Doc installed make everything appear 5 inches to the left of where it really is. But, other than the first shot, the sniper's shots consistently land several inches to the right of the intended targets.