Other mistake: When TJ goes to get the Phantom Ranger's ruby, he is standing on top of the battery pack on the Turbo Megazord. There are no other places for him to stand. After he destroys and knocks off the battery pack, in the next shot he is still standing in the same place, but there is nothing for him to stand on.
Deliberate mistake: Monkey Bulk & Skull are driving Lt. Stone's car. From inside shots of the car, Monkey Bulk's head doesn't go above the headrest. From outside shots, we can see the guy who was driving the car - his head is way above the headrest, and he's wearing a frizzy fur costume (Monkey Bulk & Skull's fur is very fine).
Plot hole: In the first episode of series 4, we are told that the Power Chamber was directly below the Command Centre. In Hogday Afternoon, part 2, at the end of series 3, the Command Centre was completely destroyed - so how could the remains of the Command Centre be next door to the Power Chamber?
Continuity mistake: The space shuttle at Nasada - first it is below ground (as shown by the little amounts of light), then it is in the open (we see the Rangers get inside the shuttle, and it is a sunny day), and then we see the shuttle be raised up from the underground.
Continuity mistake: Only a minor mistake - when Japanese footage is used, the Rangers, Elgar, Rygog, and Porto look slightly different - for example, Elgar & co. look more menacing and detailed (compared to their American counterparts), whereas the Rangers costumes are made of a different material.
Continuity mistake: The Rangers try to use the Rescue Megazord's Artillery Power to defeat Divatox's monster. After it fails, the monster blasts energy at the Rescue Megazord - at which point its shoulder-mounted Artillery cannons disappear. They reappear again in the next shot.
Continuity mistake: One at a time, the Rangers jump down a tunnel into the Phantom Ranger's service tunnels. After TJ has jumped down, watch Carlos - his position changes between frames, and the camera is on him the whole time. First he is facing the hole, next he has his back turned - yet we do not see the movement.