Wonder Woman was shown in the pilot to be able to fly, but she doesn't use this power to escape the pit with the slick ramp where she is "trapped".
When Colonel Wilcox plays a recording of Baffles' demands, a close up of the tape player shows four buttons. Then, when a wide shot of the viewscreen is seen with the Super Friends in front of it, the player now has five buttons.
At the 20:00 mark, Batman's chest insignia disappears in the close-ups, reappears in the longer shots.
When Superman arrives at the balloon, he finds the box of kryptonite covered with a blanket. The narrative does not explain that this is a lead blanket, and it only starts to harm him after he removes it.
After the lithographs disappear in the museum, someone mentions that this happened while the guards were on duty and Superman was in the museum. It wasn't Superman who was in the museum per se, it was Clark Kent, Superman's secret identity that no one is supposed to know about.
When Superman comes to rescue Wonder Woman from the pit she fell into, instead of flying down to get her, he rips a tree out of the ground so she can climb up it.