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)
Continuity mistake: When Mariposa is skydiving out of the plane, any time he's seen from afar, he's wearing a black oxygen mask. When the camera is closer to Mariposa, he's not wearing a mask. However, when he lands, he is wearing a mask.
Visible crew/equipment: After Wonder Woman rescues Nadia's boyfriend by tossing the two bad guys off screen, you can see the shadow of a stage hand adjusting a prop of some kind. This can be seen directly behind Wonder Woman as she's grabbing the rope to go and tie the two bad guys together.
Continuity mistake: Wonder Woman jumps through a window, and all of the glass smashes out, everywhere. In following shots there is no glass on the floor or the surrounding area.
Revealing mistake: When Diana is supposed to cut the power cables to stop the timer, just before she cuts the cable, you can see that all the cables are already cut and have a large, obvious seam in each of them. Then, when her hand goes through them, they all cut right at the seams.
Deliberate mistake: When Wonder Woman is bouncing around in the padded room, there's one part where you can tell the stunt double is not Wonder Woman.
Continuity mistake: When Wonder Woman tries to escape from the building, she's in the room with the padded floor and walls. Her heels are missing from her Wonder Woman boots, but they were on when she was in the hallway.
Continuity mistake: When Steve lands his plane, all you can see in the background is what looks like a wide open desert. However, when he comes to a stop, the jet is now in the middle of a completely different background and there was not sufficient time for it to go from the desert to this location in such a short distance.
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.
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.