Explanation of the screen scroll warp glitch (how to do it was not discovered by me, I read about it on some website).
On the last castle, right at the entrance, if you run and duck just before hitting the left side of the screen, you'll find that it's missing the lower invisible block, so Alex starts to "get in" the left side of the screen, until it scrolls. This causes the game to bug a bit, basically you stay on the same screen, but the enemies and items have shifted 1 screen. You can keep doing this and they shift 2 screens, 3 screens etc, until you can have the enemies from the last screen on the first screen, and then the enemies from the next "level". If you do it again it will reset the game, if I remember well.
This would be useful to get to the screen with the princess, but I couldn't get it to work because of the way the last castle is modeled.. The princess is on an upper floor, and you can only make it loop to the same or lower floors. Something like that. Here is a test movie, and the map of the last level (janken's castle).
http://dehacked.2y.net/microstorage.php/info/34750257/alexkiddmw-foda-v13.mmv
http://www.alex-kidd.com/miracleworld/maps.php
The glitch is only possible on the last level, as much as I've tried to make it work on the other ones, there's no open block on the left side of the screen on these other levels...