Continuity mistake: When Jaimie and Kevin walk to the arcade games, the boardwalk is in shadow. An instant cut later, it's in the light. (00:04:20)
Revealing mistake: After the explosion we see a shot of the fire in the second story window, and when Wonder Woman leaps up to the window the smoke is going into the window instead of out, which reveals it's shown in reverse. The boots she's wearing are also flats which then change back to heels.
Visible crew/equipment: When Jaimie greets Diana for the first time, the filming team and cameras are reflected on her yellow helmet.
Continuity mistake: Mr. Ketchum is talking with Donalsen in broad daylight when he hears his car being wrecked. When he arrives at the place, it's night time. One can see the lights of the cars zooming behind in the darkness.
Continuity mistake: When Wonder Woman spins around before the skateboard chase, the skateboard points in a 5 o'clock direction. When she transforms, it points in a 7 o'clock direction.
Revealing mistake: The safety platform which Wonder Woman is holding to simulate she is skateboarding is visible on the left side of the screen.
Continuity mistake: During the skateboard chase, Wonder Woman is either on the right lane (stunt shots) or the left lane (actress shots).
Revealing mistake: Wonder Woman's stunt is very noticeable during the skateboard chase, mainly because of her darker skin colour.
Visible crew/equipment: Several stage lights or lighting screens reflected on the side of the door when Diana arrived at the fence. (00:29:52)
Revealing mistake: Wonder Woman jumps to a rooftop and sneaks through the skylight to spy on an office. A hole in the ceiling of the studio set gives away it's not the sky, but a set she's in. (00:33:00)
Continuity mistake: When Darrell and Dr. Sylvia Stubbs are in the car, her left arm is lowered but swaps to resting on the window between shots. (00:36:35)
Revealing mistake: The stock footage of the boat is a flipped shot. (00:37:10)
Visible crew/equipment: When Darrell and Dr. Sylvia Stubbs arrive in their car, a cameraman in blue, a stage light, and filming equipment are reflected in the side-view mirror.
Continuity mistake: When the cop with the fish is busted, he steps in his car, which has a rear-view mirror. When WW stops him, the mirror is gone.
Continuity mistake: When Wonder Woman picks up the envelope, the way she holds it plus the paper inside changes between shots. The way the papers are placed also changes.
Revealing mistake: Both underwater scenes, which take place in the ocean, are of an obvious water tank, where the walls, tubes, and edges are visible.
Continuity mistake: On the boat, when Wonder Woman spins into her wet suit, it's a sunny day. A shot later, it's a cloudy day.
Revealing mistake: At timecode 00:32:04, Wonder Woman launches a thug up on a beam. One can easily see (and deliberately omit) that the shot has been played backwards and he really is falling down. The problem is, the shot is reused again at 00:32:24, though now it is played in its normal sequence and the man falls off the beam.
Continuity mistake: Wonder Woman dives in the water wearing red shoes, but a shot later she wears swim fins.
Revealing mistake: During the opening scene, when the cops follow the truck, skid marks from previous takes are visible.
Answer: The transformation twirling was invented for the 1970s TV series only, to explain her quick change from Diana Prince to Wonder Woman. However, it would have been nice to do a little spin homage in the movie.