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."
Other mistake: When the two dollar bill engraving plates are being stolen from the Bureau of Printing and Engraving (in reality it's called Bureau of Engraving and Printing), in the closeup of the plates we see the obverse and reverse sides do not look like the images on real two dollar bills of that era (perhaps this was deliberate, but still an error).
Other mistake: When Diana and Etta have their picture taken by Wotan in disguise, Diana makes eye contact with Wotan and in the extreme closeup of Diana's eyes we see that Lynda Carter is wearing modern contact lenses under her eyeglasses.
Other mistake: After Wotan's arrival on the Virginia beach, there are two closeups of Wonder Woman leaping into the air and the "boots" she's wearing aren't actually boots, they are shoes with the high boot part layered over them, and when she's on the beach she's wearing the flat boots.
Revealing mistake: When one of Wotan's fellow Nazis in the rubber boat starts shooting toward Steve, in the closeup of Wonder Woman deflecting the bullets, one of the wired remotes that control her bracelets' sparks can be seen in her right hand, and as she starts walking toward the camera we can also see the other remote in her left hand.
Visible crew/equipment: After Wotan arrives on the beach Wonder Woman sees the other Nazi with a gun, so when she leaps into the air and lands in front of Steve we can see crew/equipment at the left side of the screen (widescreen version).
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.
Visible crew/equipment: When Hank kicks Steve down the basement stairs, in the following shots the shadow of the boom pole/mic is moving around on the wall, at the left side of the screen. Then after Steve picks the lock on the chain he opens the back door, and the shadow of the boom mic is moving at the top of the screen.
Other mistake: In the two closeups of Steve's two dollar bill being held first by Steve and then by Diana, we can read "1963 A" and the name "Henry H. Fowler" Secretary of the Treasury during Lyndon Johnson's administration, as it appears under the red seal, even though this takes place in 1942.
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.
raywest ★