Significant changes (bug fixes and features) will be listed in the release notes, in /Developer/Documentation/ReleaseNotes/AppKit.html, Foundation.html, and others.
As far as the exact reason why a given Mac OS X app won't run on Public Beta --- it might be because it's using new APIs, or it might be because nib files or other resources were resaved and they include incompatible changes. There might be some clue in the console.
Ali