After playing it quickly, I noticed that some glitches in Diamond aren't present in Jade, besides the aforementioned saving one:
- Pressing A+B+Select+Start does not crash the game
- Pressing Start after the Game Over screen does not crash the game
Calling secret Denjuu still crashes the game, though.
This multi-bug patch in Diamond MIGHT work on Jade, but I haven't tried it. I said might because the menu coding seems to be different in Jade, judging from the functional save feature, which is in the same ROM bank as calling secret Denjuu. Don't complain to me if this doesn't work.
Anyway, I wonder if the first two bugs in Diamond are related, since in both cases, the game goes to the first screen. Since the Smilesoft/Natsume/et al logos are removed in the bootlegs, this is probably what has to do with it, but in Diamond, apparently the game tries to go to a screen that doesn't exist, while Jade does this properly. This is just my theory, I haven't looked into the coding, but it would make sense.
On an unrelated note, the dialog seems to be the exact same so far, even having the same typos like "I' ve even got a headache" (notice the space after the apostrophe). I'm surprised that it's consistent, actually.