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.
Other mistake: Episode 13-12: "Shadow (2)." When Cruger is challenged to defeat 100 robots, a red countdown meter appears on the screen, ticking down each time Cruger dispatches an opponent. When the counter is at 21, Cruger slices his sword at a robot, which then goes down. But the counter stays at 21 and only goes to 22 when he slices at the next robot. Every robot in the sequence goes down after a single hit from Cruger's sword.
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."