Goofs

When the elderly woman is shooting at Wonder Woman with a Thompson sub-machine gun, the front muzzle grip of the machine gun repeatedly switches between having rifle front grip and a pistol front grip.

In the bank robbery scene, the two bad guys with cases are initially seen shooting towards the door of the bank as if they'd just left with the money and are making their escape. However, when Wonder Woman leaps over the car to intercede, they are shown coming out the doors with the cases and exchanging gunfire again.

At the end of Wonder Woman's fight with Marcia, a clock in the hall reads exactly 11:00. Over two minutes of conversation follow, but at the end of the scene, the clock still reads exactly 11:00.

When the Uboat explodes, a Japanese flag is visible on the conning tower. (likely taken from McHale's Navy)

The initial close-up of the German XV-13 bomber's cockpit, and the shortly afterwards full-length sidelong view, do not match. At first, the so-called XV-13 appears to be a fairly rickety nondescript aircraft, but moments later is revealed to be a sleek Heinkel He III, a German medium bomber from the Second World War era.

A twin-engine bomber of the Second World War era, such as the so-called XV-13, which is actually a Heinkel He III, couldn't fly a bombing mission with only a pilot. A Heinkel He III required a crew of five, including machine-gunners, and a navigator. The pilot couldn't do the bomb-aiming, this required a bombardier, operating controls far beyond the pilot's reach. The whole XV-13 mission is therefore pointless.

It was mentioned that a squadron of P-38's stood ready to intercept the German bomber, but that they were no match for the lone XV-13. The so-called XV-13 turns out to be a Heinkel He III, which was a medium bomber, no match whatsoever for a Lockheed P-38, which was a fighter, popularly known as a Lightning, legendary for having been dubbed 'fork-tailed devil' by the Germans. On top of this, this XV-13 only had a pilot, no machine-gunners defending it (a Heinkel He III required a crew of five). Incidentally, in the show's last scene, in Steve's office, one of those black-and-white portraits show a P-38 Lightning, distinctive in shape for having a twin-boom configuration (hence its nickname). Built to attack, with a top speed of roughly 660 km/h, about one-third faster than a Heinkel He III. Imagine a squadron of those in pursuit of one defenseless bomber.

The body of the newspaper article with the headline starting "Steve Trevor Recovering" is composed of generic, almost nonsensical prose, and the same paragraphs are repeated in neighboring columns.

NOTE: This is only a "goof" in this current era with far more sophisticated means. The shot in question lasts two seconds. Viewers in 1975 saw it once on smaller, lower-definition TV sets that could not pause, rewind, record, or zoom in on the shot. Repeats were very infrequent, and home media or streaming did not exist.

Steve's interception of Drangel was a secret mission, so why was there a newspaper article about him missing and, later, about his recovery in the hospital?

UPDATE: The mission is over. It no longer needs to be a secret.

Ashley, at one point, refers to Diana as "Wonder Women".

UPDATE: This is not a goof. Ashley Norman knows her only as Wonder Woman. Lynda Carter's "Diana Prince" persona is introduced after Ashley has left the story.

In the Amazon hospital where Steve is being cared for, one of the Amazons glances at the camera although there's nothing to look at in the scene in that direction.

During the "Bullets and Bracelets" sequence, when Diana's opponent is injured and grabs her wrist, you can clearly see the remote control, used to make the bracelets flash, that she is holding in her hand.

Obvious dummy when Princess Diana is running with an unconscious Steve Trevor in her arms on the beach.

During the first 3 episodes of the 1st series when Yeoman Diana Prince would spin into Wonder Woman, her Amazon bracelets are missing after the transformation.

When Marcia and Wonder Woman fight the overhead shots of the altercation are noticeably darker to obfuscate the faces of the stunt women performing in the scene.

During the athletic competition, one of the foreground Amazons is wearing a wedding ring.

When Oberst is flying over Rio de Janeiro, a graphic says he is 4,771 miles south of Washington D.C., but Rio is actually south-southeast from D.C., not south. The distance is approximately correct, but if the direction was due south, Oberst would have been over the Pacific Ocean west of Chile.

Even in the realm of fantasy, much defies logic. Wonder Woman jumps out of her Invisible Plane to enter the XV-13 German bomber down below. Her own plane is therefore without a pilot, and will crash. Von Blasko, the German pilot, is knocked unconscious. She then dive-bombs a German U-boat with the hijacked German plane. And flies away in her Invisible Plane. Von Blasko, it is later learned, ended up in prison. But who kept her Invisible Plane in the air, and how did she get back into it after setting the German plane on its nose-diving course to strike the submarine? And how did she get the unconscious German pilot out of the doomed plane? When she flew away in her Invisible Plane, it being see-through, it's clear nobody else but Wonder Woman was in there.

When Wonder Woman leaves Marcia to stop the bombing, she leaves her still in her magic lasso.