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: 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.
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 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.