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: When Wonder Woman launches the robot away, the actor playing him is swapped for a rubber doll that bends awkwardly.
The Return of Wonder Woman - S2-E1
Revealing mistake: When Trevor's copycat is about to punch Wonder Woman, he is replaced by an obvious stunt double. The shot then cuts to the real actor, which underlines the difference between both.
The Return of Wonder Woman - S2-E1
Continuity mistake: When the bad guys are beating Trevor's ass in the park and Wonder Woman spins around to transform herself, there's a man kneeling down behind her who disappears between shots.
The Return of Wonder Woman - S2-E1
Revealing mistake: The jet is supposedly taking a nosedive, but one can see the horizon line behind is also tilted, revealing the camera trick.
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.
Continuity mistake: Wonder Woman stops a tank with its tracks moving, but when the shot changes, they're still despite the motor running. This swaps back and forth.
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 Man Who Could Move the World - S2-E3
Continuity mistake: Trevor wipes the dry leaves off the billboard with his foot. A shot later, they're covering the billboard again.
The Man Who Could Move the World - S2-E3
Revealing mistake: When Ishida lifts the phone up in the air using his mind, the cable is visible.
The Bermuda Triangle Crisis - S2-E4
Visible crew/equipment: When Ray Manta tells Trevor and Diana they have to think about his offer, the shadow of the boom mic is visible on the wall behind. (00:31:15)
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.
The Bermuda Triangle Crisis - S2-E4
Revealing mistake: When Wonder Woman spins to transform from her wetsuit back to her costume, it's the previous transformation played backwards. Check how she moves counterclockwise and how her hair moves unnaturally.
The Bermuda Triangle Crisis - S2-E4
Other mistake: When the plane is leaving, its tail number is backwards, revealing the shot was flipped.
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: Hamlin Rule, the bad guy in this episode, is a singer. When he sings, his lips frequently don't match the words being sung.
Answer: Yes, on the first episode of season 2, she is shown on the island, when another plane crash lands, she says, "They sound different from WW II". Later in the same episode a woman gathers background information on Wonder Woman. The woman says, "From 1942 to 1945, she helped the Allies win the war."