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: 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.
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.
Formula 407 - S1-E12
Continuity mistake: After Diana sidesteps Antonio's advances, when Wonder Woman rushes off to save Steve she's grabbed by one of the Nazis who holds a chloroformed handkerchief to her face with his right hand, but in the closeup it's in his left hand, and then it's back in his right hand.
Wonder Woman in Hollywood - S1-E14
Continuity mistake: After Bremer "shoots" Wonder Woman, when Jim runs after Bremer and tackles him to the ground Jim's stunt double is wearing dark rubber sole shoes, even though Jim is wearing brown dress 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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