The Return of Wonder Woman - S2-E1
Factual error: When Steve gets attacked by the bad guys and Wonder Woman shows up, the lady in the car pulls out a camera and films the event. She sits still, the car isn't moving, and she does all the filming from the same position. However when she watches the playback, the film shows footage from multiple angles and varying distances, which is impossible because she and the camera were in the same spot the whole time.
The Return of Wonder Woman - S2-E1
Visible crew/equipment: While the jet is flying over the Bermuda Triangle the steward releases the gas into the air, and when Steve rushes toward him in the wideshot we can see a crew member wearing jeans and a blue shirt, at the right side of the screen.
The Return of Wonder Woman - S2-E1
Continuity mistake: Quite a few of the exterior shots of the jet which Steve is on are flipped shots (including the landing closeup), note the tail number "N207L" is backwards.
The Return of Wonder Woman - S2-E1
Revealing mistake: After the steward releases the gas on the jet everyone passes out, and in the second exterior shot of the jet as it rocks from side to side, we can see the circular frame of the window from which the jet was being filmed, at the bottom right corner of the screen (this shot is flipped).
The Return of Wonder Woman - S2-E1
Revealing mistake: During the scenes on the jet with Steve and the others, before landing on Paradise Island and when the Amazon women are aboard, the end of the cabin and cockpit sets are visible at either the right or left side of the screen in some shots. (Widescreen version).
Visible crew/equipment: When Joe Atkinson walks into Steve's office and comments that during WWII he "was wrapped in a cloak and carrying a dagger for the OSS," in the next shot the shadow of the boom mic is moving on the wall, at the top right corner of the screen.
The Man Who Could Move the World - S2-E3
Continuity mistake: Steve complains that he can't steer the Jeep. The Japanese doctor is using mind control to keep Steve from being able to control the Jeep. However, in several shots, Steve can easily be seen steering the Jeep despite the doctor's continued control over it.
The Bermuda Triangle Crisis - S2-E4
Revealing mistake: When Wonder Woman drops a mine into the water, she's supposed to be dropping it into the ocean. However, you can see a drain plug of some sort in the background and the "ocean" is obviously a pool, or similar.
The Bermuda Triangle Crisis - S2-E4
Continuity mistake: Steve and Diana steal wrinkled uniforms from a clothesline. However when they put the uniforms on, they're perfectly pressed.
The Bermuda Triangle Crisis - S2-E4
Continuity mistake: After Wonder Woman gets Steve out of the tree, you can see a big shrub in the foreground on the right side of Steve's body. When the camera changes angles, the shrub is suddenly gone.
The Bermuda Triangle Crisis - S2-E4
Continuity mistake: Steve's parachute moves around, even though it's flat on the ground and no one moved it. After Wonder Woman rescues Steve from the tree, Steve is laying on the ground motionless and unconscious. His parachute moves around between the time Wonder Woman walks away and Diana returns, even though nothing could have moved it. It wouldn't be so obvious, except that the material is red and white, so when it changes, you can really tell.
Continuity mistake: When Diana escapes from the guy who had kidnapped the boy, she runs into the woods wearing a dress. When she starts to turn into Wonder Woman, she is somehow now wearing pants just before she changes into Wonder Woman.
Visible crew/equipment: When the hit-man is loading his gun in the alley in preparation to kill Diana, a crew member is reflected in the storefront "Humburgers" window.
Audio problem: Harlin Rule, the bad guy in this episode is a singer. When he sings his lips frequently don't match the words being sung.
Audio problem: When Harlin Rule is playing the flute by the pool, he stops playing it, but the music continues even after the flute is away from his lips.
I Do, I Do - S2-E8
Continuity mistake: When Wonder Woman is chasing the golf cart, in the close-ups, the golf bags are not moving, but in the far-away shot, one golf bag is bouncing all over the place. When they zoom in, it's not moving again.
Mind Stealers from Outer Space: Part 1 - S2-E10
Continuity mistake: The doctor's arms change positions, and holds a stethoscope that disappears and reappears as he speaks with Diana Prince.
Revealing mistake: When the toy aeroplane, which is supposed to be remote-controlled, attacks Wonder Woman, in a closeup shot you can see the wires which are actually controlling it.
Revealing mistake: Wonder Woman lifts the rear of the toy maker's van. During the pan from the rear wheel to Wonder Woman you can see the jack holding the van up.
Continuity mistake: Diana spins herself into Wonder Woman before she enters the gym. Watch the trash can behind her - it suddenly disappears. Additionally, in the widescreen version, a security guard can be seen standing between the car and metal door, though surely Diana would not transform into Wonder Woman in right front of someone (the guard is not visible in the original fullscreen version). (00:35:45)
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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