In "Fausta: The Nazi Wonder Woman", both Wonder Woman and Steve Trevor are completely dry immediately after climbing out of a "water trap".
In "Fausta, The Nazi Wonder Woman", there are two Wonder Woman transformations. After both of them, Wonder Woman doesn't have her bracelets, though she's wearing them in the following scenes. One of these transformation sequence is used again in "Wonder Woman meets Baroness Von Gunther".
During the car chase, at one point the rear window of the taxi is cracked/splintered but in a later shot, the window is perfectly clear.
A map of Europe is shown in "Fausta: The Nazi Wonder Woman" which takes place in 1942 - however Germany, Poland, and other European countries are shown with their 1970s boundaries. If one looks carefully, one can even see the dotted line separating the post-WW2 East and West Germany.
A Nazi officer compares Wonder Woman to Dale Evans. While it's not impossible that a German would be familiar with an American actress, Ms. Evans was not a star until after 1942, the year in which this episode was set.
The distance from Washington DC to the closest German held territory in 1942 was about 3,500 air miles. The plane used to fly Wonder Woman there was a single engine aircraft that lacked the range to make such a flight. Aircraft such as the one shown had a range of 700-800 miles. Additionally, this trip is made several times as if it were a local flight with characters being in Germany or Washington in just a few hours. Even in modern times with jet aircraft, such a flight is about 9 hours. In 1942, it would have taken over half a day or about 16 hours to make such a flight, and very few aircraft were capable of doing so.
When Steve and Etta are chasing the car in a taxi, Steve takes a shortcut by turning right off the pavement onto a dirt road. After reaching a dead end, they return to the paved road and turn left to go back in the direction they had come from, yet a minute later they are adjacent to the plane the Nazis are using.
Charlie when first talking to Steve circa 1942 says he is going on a mission over Berlin. While the British had been bombing it since 1940, the US Army Air Force did not bomb Berlin until 1943.
Prior to taking off, a character removes the US insignia from the side of the airplane revealing a German insignia. He fails to remove the US insignia on the wings, which defeats the purpose of revealing the side insignia.