Going through the episodes of Mighty Morphin Power Rangers Season One and Two that had footage that Toei shot for Power Rangers that was not in Zyuranger or Super Sentai at all, I notice some things. Not only did they get the new monster suits from Rainbow Productions, it seems that they also got random props. The strange thing about the footage was a common theme of objects being Blue and having Billy's Triceratops symbol on it.
In Wannabe Ranger, Kimberly hands Billy a mirror, we can't really see it good but we can see it is blue. At a closer look, it has the Triceratops symbol.
In the Zyu 2 footage, Billy hands it to the fake Tommy and we clearly see it has the Triceratops symbol but seems smaller symbol than the one in the American prop.
In "Grumble Bee," Alpha made a special weapon for Billy to combat the titular monster. Here is the Japanese footage.
Here is the American footage. It looks like the same exact prop.
In "Bloom of Doom," Kim is given a new weapon by Zordon. Here is the American appearance.
Here is the Japanese footage version.
In "Green Dream," the Sword of Power comes out of nowhere seemingly. Apparently the six Rangers combining their powers together made this sword. It was not established before and never mentioned again. I think it did get a mention in the official magazine and trading cards but that was it.
It looked different from the one in the Zyu 2 footage, where it looked like 3 diamonds and 'horned' while the American prop looked more round and bulbous.
Here is the American prop that looks more bulbous and round.
Here is something curious:
In the episode "Flea or Not to Flea," Billy makes a spray can to make Jason stop itching. It says "Billy's" and what looks like "Pow," there probably more but I couldn't get a good enough look.
In the Zyu 2 footage, the prop looks exactly like the one in the American footage but since the Blue Ranger is covering the top of the can, you can't see if it says "Billy" or not. I doubt the Japanese put Billy's name in it but maybe since it was meant for Power Rangers, maybe they did. But there is no way to prove it. From what the writers said at PMC3, they didn't know what the footage was from. It is most likely the Japanese just made the footage according to Saban's guidelines: Blue being an inventor, Yellow having female stances, and Green and Pink having a relationship and Green loosing his powers. And they didn't have input with the actual writing. The writers were probably handed the footage and they just wrote just like the other Sentai footage.
The letters on the can Billy used in "Flea or Not to Flea" looks like font used for the batteries used in the footage used in "The Mutiny Part 3."
The American prop matched more or less.