Wonder Woman steps out a window in the middle of the night. On the ledge it's broad daylight.
Blankenship says Eisenhower is supposed to meet with a special forces officer, but the first US special forces were not established until 1952. Prior to that, there were components that would become special forces, but they were not referred to as such.
The Q Clearance referenced at the beginning is a type of security clearance that was not established until 1947 when the Atomic Energy Commission was formed to take over the Manhattan Project. So it did not exist during WW2 as shown, and it is a specific clearance type for atomic secrets which was not involved in the show.
During the car chase scene, tires screech on the dirt road.
When Wonder Woman deploys her "golden" lasso it is obviously plain brown rope.
The beauty contestants arrive wearing custom t-shirts with their names but the thermoplastic resin that made these iron on letters possible was not invented until the late 1960s.
At the beginning this is said to be taking place May 1942, at a time when Bazookas (man-portable rocket launchers) were not available. The first Bazookas were not in production and issued until June 1942. The first Bazooka model was the M1, with a forward hand grip; the one used by the Nazi assassins did not have a forward hand grip, and so had to be one of the many following models produced starting in July 1943.
Near the end, after Burns launches the first explosive, General Blankenship points and yells where the shot came from, he says the name "Diana" instead of "Wonder Woman."
When Steve and Linda first show up on base, Steve makes accusations about a spy on base, even openly disagreeing with the Colonel. A Major, such as Steve is portrayed as, would never speak so disrespectfully to someone two pay grades above him. Doing so, Steve could be brought up on military court martial for disrespecting a superior officer.