The Feminum Mystique: Part 1 - S1-E5
Continuity mistake: When Diana comes home and spins into Wonder Woman there's a plant on the table under the mirror, but when she walks out of the kitchen with Drusilla that plant is on the floor. Then, note the only thing atop the hutch is a crystal basket, but when she changes back to Diana Prince two more large items are atop the hutch, now the plant is back on the table, and a tall lamp has suddenly appeared beside the chair.
The Feminum Mystique: Part 2 - S1-E6
Continuity mistake: When Wonder Woman is spinning the XPJ-1 around, she's seen approaching the jet with her hands empty and her lasso on her side where it usually is. As the scene progresses, her golden lasso magically appears in her right hand even though she never reached down to pick it up.
The Feminum Mystique: Part 2 - S1-E6
Continuity mistake: While Nazis are invading Paradise Island, back at the deserted warehouse when one of the Nazis brings Drusilla a hot meal he slams the door shut, but when Drusilla hits him in the stomach the door is suddenly wide open, but when she rushes out of the room the door is closed and she pushes it open.
The Feminum Mystique: Part 2 - S1-E6
Continuity mistake: When Wonder Woman is pushing the XPJ-1 around, tyre marks from previous takes suddenly appear on the runway before the plane actually makes those turns.
Wonder Woman vs Gargantua - S1-E7
Continuity mistake: After the Nazis capture Steigler, while they're at the oil refinery Gargantua is in a cage behind them. When Erica blows the whistle, the gorilla reaches through the bars and grabs a large cardboard cutout of Wonder Woman, which was leaning against the wall, but the problem is that in the previous shots that cardboard cutout was not there.
Wonder Woman vs Gargantua - S1-E7
Continuity mistake: An alarm button vanishes from the safe house room wall between shots.
Wonder Woman vs Gargantua - S1-E7
Continuity mistake: When Diana is left in the office by Steve, she changes into Wonder Woman. When she does, watch the open folder and pen on the desk on the left side of the screen. When she becomes Wonder Woman, the pen disappears.
Wonder Woman vs Gargantua - S1-E7
Continuity mistake: When Diana changes into Wonder Woman in Dr. Osmond's lab, the green stool jumps from one location to another in the process and the silver stool disappears.
Wonder Woman vs Gargantua - S1-E7
Continuity mistake: After Gargantua slams Steigler into the desk, Steigler's body can barely be seen on top of the desk and looks like most of his body is behind the desk. However, when the MP enters the room, Steigler is shown to be on top of the desk and his whole body can be seen. Gargantua didn't move him and Steigler is unconscious.
Wonder Woman vs Gargantua - S1-E7
Continuity mistake: When Wonder Woman arrives at the warehouse where Steigler is being held, as she's using her lasso to scale the building the high heels on her boots have vanished, and they're now flats. This switch also occurs in previous shots, as well as at the start when Erica Belgard is disguised as Wonder Woman.
Continuity mistake: When Wonder Woman chases after Benson her boots are flat and then the heels appear. It happens again later, while The Falcon tries to reach Professor Warren.
Continuity mistake: When Wonder Woman approaches the blackboard, it's filled with formulas. A shot later, half of them are already erased before she starts using the eraser.
Continuity mistake: When the sniper tries to kill the scientist, it's pitch-black night. When Wonder Woman jumps to catch him, it's daylight.
Continuity mistake: Wonder Woman jumps out of the hospital window face down but lands feet first, seemingly to allow for the stuntwoman to land on a mattress.
Continuity mistake: When Steve and Diana are off the coast of Virginia, they share binoculars to watch for three men coming ashore in a rubber boat, and when Steve raises the binoculars to his eyes the lenses are either extremely cloudy or the lens caps are on (it reflects no light), but in the following shot when Steve lowers the binoculars the lenses are perfectly normal. Then when Steve hands Diana the binoculars the lenses are still normal, but in the following shot when Diana lowers them it's once again extremely cloudy or the lens caps are on.
Continuity mistake: In the first two closeups of Steve's two dollar bill, the serial number on the bill is "A16452841A", but when Diana kisses the bill and leaves a lipstick mark, in the next closeup it's actually a different two dollar bill with serial number "A77148841A."
Continuity mistake: When Wotan and the other two Nazis arrive in the rubber boat, during the scuffle Steve is wearing boots, but his stunt double is wearing completely different shoes.
Continuity mistake: Wonder Woman is on the beach and removes her tiara. A shot later, she's in a studio set.
Judgment from Outer Space: Part 1 - S1-E10
Continuity mistake: When Wonder Woman is about to enter the spaceship, we see a close-up of Wonder Woman's lips because she whistles the tune that opens the ship's door. At the beginning of the next episode (which takes place a few minutes later in the story's timeline), we see another close-up of Wonder Woman's lips. This time, she's wearing lipstick, although she hasn't had time to put any on.
Judgment from Outer Space: Part 1 - S1-E10
Continuity mistake: During the fight at the gardens and the later fight at the library, Wonder Woman's high-heel boots swap to flat shoes.
Answer: There is no logical reason. Any normal person would notice these type of absences. The show employs a "suspension of disbelief," which is a literary device where the movie audience or a book reader accepts that certain things are unreal for the sake of the story to be told. It is similar to no-one noticing that Clark Kent looks exactly like Superman because he wears glasses.
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