Continuity mistake: Up until Green No More in Series 2 (where the Green Ranger powers are destroyed), the Green Ranger's overshield constantly changes between solid-looking metal to flimsy-looking cotton. This is the most obvious difference between the Japanese and US footage.
Continuity mistake: When in Tank mode and Megazord mode, the order in which the Rangers sit is: Billy, Trini, Jason, Kim, Zach. When switching between Tank mode and Megazord mode, Trini and Kim are switched - they are then back to their original seats once the Megazord has been formed.
Plot hole: How were the Rangers (minus Jason) able to form the Megazord if Jason wasn't there to summon the Tyrannosaurus (not to mention Jason's morpher being in Goldar's possession)?
Audio problem: The Megazord throws the Dragonzord into a nearby mountain. As the Dragonzord tries to get back onto its feet, Jason, from the cockpit of the Megazord, tells Tommy to "give it up." A man who sounds absolutely nothing like Tommy replies "No way."
Other mistake: In the scene where Tommy is proving himself to Goldar on the beach against the putties, Tommy stares down the last remaining putty and makes a charge towards him. In the wide shot of Tommy charging towards the putty, one of the "dead" putties on the ground lifts his head off the ground slightly, almost as if he is watching the action unfold. (00:09:05)
Other mistake: After the teens leave the command center, Rita sees this and orders the creation of her Putties. Her henchman slaps down a few things of clay into a mold loosely, that then show the perfect figurines of the putties coming out of them. However with the shape of the mold, there is no way that the clay would come out in shapes like that or with that detail. (00:11:35)