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.
Judgment from Outer Space: Part 1 - S1-E10
Visible crew/equipment: When Wonder Woman shows up at the Library of Congress, in the overhead shot of her leaping over the bookcase, an unfinished part of the set is visible at the right side of the screen. Then after Andros has been taken from the Library of Congress, in the following shot at General Blankenship's office, we can see the end of the set wall at the right side of the screen (widescreen version).
Judgment from Outer Space: Part 1 - S1-E10
Visible crew/equipment: When Steve is telling Diana about the full scale search for Andros while they're in Steve's office, just as Steve sits down the camera pans to the left and we can see the shadow of the boom mic moving at the top left corner of the screen, as well as the end of the set wall at the left side of the screen.
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 2 - S1-E11
Audio problem: Wonder Woman whistles inside Andros' ship, but her lips do not open slightly. They remain closed.
Formula 407 - S1-E12
Other mistake: At the start, the episode's textbox reads, "Fort Frazier Ordnance Testing Facility" with correct spelling, but in the next shot the base's sign reads, "Fort Frazier Ordinance Testing Facility" when it should actually be "Ordnance."
Formula 407 - S1-E12
Revealing mistake: After Major Keller leaves in the car with Steve and the formula, when Wonder Woman rushes in front of Maria to protect her when she's being shot at, the wired remote that controls her bracelet sparks is visible in her left hand, as she moves her arms to deflect the bullets.
Formula 407 - S1-E12
Visible crew/equipment: While Lydia is being held at the shack, when Steve is with Professor Moreno he looks out the window at three Nazis on the street down below, and in the overhead shot of those three walking away from the car, their three T-marks are visible on the ground.
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.
Visible crew/equipment: After Lampkin tells his buddies to deal him into the poker game and how they'll clean out Diamond H cattle, when it cuts to the Maria and Charlie doing dishes, there is something at the left side of the screen that moves with the camera, which should not be seen onscreen (widescreen version).
Visible crew/equipment: After Wonder Woman cautions JP about Lampkin, when JP tells the kids about Maria's apple pie note the open cabinet door over JP's shoulder, presumably to prevent reflections. After Jeff admits to being Lampkin's informer, when JP walks over to Jeff that cabinet door is closed and now we can see the reflections of array lighting/equipment (then when WW walks over both doors are ajar).
Visible crew/equipment: After the children rescue Wonder Woman it cuts to her telling JP and Jeff about it, and when JP tells the kids about Maria's hot apple pie, the actor's tape mark is visible on the rug where Charlie had been standing.
Visible crew/equipment: After Steve finds out the truth about Lampkin, while the Deputy chases Steve in the jeep we can see a bit of the back end of the filming vehicle in one of the shots facing Steve, at the bottom left side of the screen (widescreen version).
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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