From Out of Nowhere: Part 1 - S1-E1
Continuity mistake: In "Chase Into Space part 2", the Rangers and Alpha were covered in dirt, and their clothes were ripped and torn. While their clothes are still slightly ripped and torn, they are now completely clean of any dirt.
Suggested correction: It's a space shuttle meant for travel to another planet (that's a whole other discussion). One would assume there would be a bathroom or some other amenities for astronauts to clean themselves up.
From Out of Nowhere: Part 1 - S1-E1
Continuity mistake: On the shuttle when the rangers first see the megaship through the window of the shuttle you can see the v-shaped tail wing sticking out of the megaship. This shouldn't be possible yet as they hadn't docked.
Continuity mistake: Bulk throws a watermelon in the air. When it lands on his head, its texture changes from darker to lighter, and the "watermelon lines" aren't as visible - this couldn't have been caused by the watermelon splitting, as half of it stayed on Bulk's head.
The Craterite Invasion - S1-E9
Continuity mistake: The entire episode, the Astro Megaship is shown orbiting the Earth, yet a few minutes after the Craterites appear, they are parachuting out of the Astro Megaships. Not only were they not shown to have grabbed parachutes when jumping out, but the Megaship wasn't even in the Earth's atmosphere.
Suggested correction: They simulate hard hats clothes and other material to take the forms of people on Earth. Considering they're simulations themselves. They created the parachutes. It would be mass suicide otherwise. Some escape plan.
The Wasp with a Heart - S1-E10
Continuity mistake: The Wasp Monster literally scares Bulk, Skull, and the Professor out of their pants when they are found by the Wasp Monster. After they have run away from the WM, their pants are nowhere to be seen.
Suggested correction: Their pants are still in front of the truck where they left them in every shot of that side of the truck. They are there.
Continuity mistake: Piranatrons have always been small and weak - their appearance hadn't changed for 2 series and a film. Yet when Quadtrons and Piranatrons are fighting the Phantom Ranger, the Piranatrons are noticeably taller and larger than normal, when standing behind Divatox. Divatox has ALWAYS been bigger and taller than Piranatrons.
Suggested correction: That is an impossible detail to notice considering she has an army of them...and they squat most of the time. You can't definitively state that all of them have been shorter than her while standing and the ones in the movie are indeed different. You can't say that just because this one time when two are standing taller than her...that they ALL are small and weak.
Continuity mistake: The police car the Grandmother steals changes - its colours, position of sirens, license plate, and the inclusion of Japanese writing on the side change back and forth as the episode goes on.
Continuity mistake: Andross shoots down a Barillian bug from behind a tree, and his Galaxy Glider is behind him. When he runs into the field to meet TJ, his Galaxy Glider is now in the open field, with there being no evidence of it moving, or being moved.
The Rangers' Mega Voyage - S1-E17
Continuity mistake: The Astro Delta Megazord is knocked to the ground, and slides past the buildings. In one shot, the Delta Armouring disappears - it reappears again in the next shot.
The Rangers' Leap of Faith - S1-E28
Continuity mistake: When the Astro Megaship enters the Jungle Planet's atmosphere, there is a strong thunderstorm going on. However, when they land, seconds later, there is a clear blue sky, and no sign of a thunderstorm.
Suggested correction: They're traveling horizontally through the clouds not down into them. Since TJ changes course they flew out of the storm.
Dark Specter's Revenge: Part 2 - S1-E30
Continuity mistake: The Professor walks in front of the Rangers, threatening the Monster. In the very next shot, he is behind the Rangers again.
Continuity mistake: Throughout the series, the Rangers' morphing has been instantaneous. Anyone who has ever been in a photobooth will know that they take a good minute or so to get through all 4 photos (which is what Sophie picks up) - it has never taken Carlos, or any Ranger, that long to morph.
Countdown to Destruction: Part 2 - S1-E43
Continuity mistake: Astronema throws Andross into some mesh panelling, and the corner pops out of the frame. In the next shot, it is back in the frame.