The lock on the basement "cell" where people are imprisoned is repeatedly destroyed, and then reused.
The binoculars used by Steve Trevor and Diana Prince have lens caps on and off in alternate shots.
At one point Wonder Woman is shown running behind a fence, but then in the close-up, she's in front of the fence.
They say that the Germans had "American towns" where they trained their spies. This was something that the Soviets did, but the Germans didn't.
At the end when Wonder Woman goes to throw her tiara/boomerang at Wotan, the close-up of her throwing it was shot on a soundstage, as the background is suddenly different from the one at the beach.
The climatic beach scene is supposed to be happening somewhere on the East coast of the U.S. in the afternoon, but the coastal shots have the California mountains in sight. What's more, the sun is over the water and since it is supposed to be the afternoon on the east coast, the sun should be on the land side, not the ocean side.
As Wonder Woman twists the pad lock to break it open, one can see that the pad lock was never actually locked.
At the end Wonder Woman's rope was suddenly much longer than normal. After she had tied up the two German agents by wrapping the rope around the two of them a number of times, she still enough to make a lasso out of the free end and threw it to catch Wotan. A rope that long would have made a much bigger bundle than what is seen attached to her waist.
The $2 bill that Major Trevor and Diana Prince look at is a series 1963 United States Note. The episode takes place in 1942.
Wonder Woman perfectly imitates the Secret Service agent's voice over the phone when talking to Major Trevor, despite having never heard it before.
When Steve Trevor escapes the restaurant basement, one can see the shadow of a boom mic when he walks out the door.
Hank Miller explains to Wonder Woman that paper money is valuable because it is backed by gold stored at Fort Knox, and that paper is easier to carry around than gold bars. The story is set in 1942, but the U.S. had abandoned the gold standard in 1934.
The phony "Hank" addresses Steve Trevor as "Major" when the phony "Maggie" hands Steve the phone, despite "Maggie" not telling "Hank" that he'd be talking to Steve.
Steve Trevor states that $2.00 bills are being removed from circulation. In fact, $2 bills remained in circulation until 1966 (and were re-issued starting in 1976 to help commemorate the Bicentennial).
Wonder Woman says she remembers Genghis Khan and Napoleon. The women of Paradise Island were supposed to have been isolated and ignorant of the outside world, so she shouldn't know about them.