Wonder Woman vs Gargantua - S1-E7
Visible crew/equipment: When the truck carrying the caged gorilla pulls into the alleyway, just as Hans and Carl exit the truck and walk away, the blue-sleeved arm of the cameraman/crew member is visible as it moves upward, at the right side of the screen.
Wonder Woman vs Gargantua - S1-E7
Continuity mistake: An alarm button vanishes from the safe house room wall between shots.
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."
Fausta, the Nazi Wonder Woman - S1-E3
Continuity mistake: After Wonder Woman is kidnapped, Steve commandeers a taxicab which has damage on its roof, but when Steve is driving the cab there's a black cloth taped to its roof covering the damage.
The Feminum Mystique: Part 2 - S1-E6
Visible crew/equipment: After the Nazis are defeated on Paradise Island, Queen Hippolyta tells her daughters that she has plans for those Nazis, and at the start of the next shot a bit of set equipment is visible at the left side of the screen (widescreen version).
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.
Wonder Woman vs Gargantua - S1-E7
Visible crew/equipment: While Wonder Woman searches for Steigler at the deserted oil refinery the Nazis force Steigler to shout for help, then when they all hide and Wonder Woman breaks into the room, the actors' two tape marks are visible on the floor near Steigler.
The Feminum Mystique: Part 1 - S1-E5
Visible crew/equipment: During the games on Paradise Island, a few trailers and two cars (one has a protective cover over it) are visible in the background, first in the opening shot and also when Drusilla rides the horse past Queen Hippolyta.
Wonder Woman Meets Baroness Von Gunther - S1-E2
Other mistake: After Wonder Woman rescues Steve and another soldier from the burning Old Virginia Stables, in the next shot the textbox onscreen reads, "Shortly therafter in Diana Prince's apartment," but the proper spelling is "thereafter."
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.
Wonder Woman Meets Baroness Von Gunther - S1-E2
Continuity mistake: When Wonder Woman calls the Dept of Motor Vehicles disguised as General Blankenship, the woman who answers the phone has long polished fingernails, but in the closeup of her going through the file box the fingernails we see are quite short and unpolished (looks like a man's hand).
Continuity mistake: When Wonder Woman lassos the two hoods who were after Steve, in the wideshot the lasso's small loop is at the left encircling the two men, but in the closeup the small loop is at the right side, then it's back at the left.
Wonder Woman Meets Baroness Von Gunther - S1-E2
Visible crew/equipment: After Diana sees Tommy in trouble on the ladder she leaves Steve with the Baroness, and when she finds a private area by the lockers to transform into Wonder Woman, the reflections of four crew members are visible at the right side of the screen (widescreen version).
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.
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).
Visible crew/equipment: When Diana and Steve meet with Dr. Barnes at the hospital, they stop in the corridor to discuss the guard's condition, and when they resume walking the actors' T-mark and two tape marks are visible on the floor, where they had been standing.
Wonder Woman vs Gargantua - S1-E7
Revealing mistake: While the circus crowd is gathered around the cage with Gargantua, there's a closeup of the gorilla as he roars and we can see the stuntman's human teeth behind the gorilla's teeth. It happens again in Gargantua's closeup while he's climbing up to Steigler's window.
Visible crew/equipment: When Wonder Woman is in the kitchen with the children telling them they should take care of themselves, a crew member's back is visible at the left side of the screen.
Visible crew/equipment: When Wonder Woman arrives at the Diamond H ranch, the housekeeper opens the front door and the reflection of lighting/equipment is visible on the glass. Additionally, there's a prominent flagpole at the front of the house with the Flag of Texas flying high, but the problem is it's being flown upside-down with the red stripe at the top, when it should be the white stripe at the top. Proud Texan JP Hadley would know better.
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).
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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