I had a bunch of personal disks that didn't read properly in a real amiga so I purchased one of those catweasel cards. The software that it comes with (PC/Windows) keeps trying to re-read the disk over and over again until it gets it successfully read. It actually worked and now I use it all the time. I was very thankful it saved some of my old game code from 1989!
Great tip! Though unfortunately the Catweasel doesn't work with NDOS disks, so wouldn't help the OP to recover his copy of Rainbow Islands.
@Jonas
Technically downloading an ADF is illegal. Whether or not you consider it immoral in light of the fact that you actually own a copy of the original disk is up to you, and I hardly think you're going to get Taito knocking on your door.
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moto