The Apple Support Discussions forum thread, started by user c9ky6qk3, has yet to offer a concrete solution, though some suggestions that may work for other users are present. The problem, as reported by c9ky6qk3:
"So I'm not sure when this started happening exactly, but my Mac stopped being able to read burned discs for some reason. I've tried discs that have audio (legal MP3's) and applications on them (also legal copies of the discs) and they show up in Finder, but as a blank disc. I'm wondering if there was an update of some sort recently that started causing this issue somehow?"
Operating system updates have been known to cause disc-reading issues in the past. The Mac OS X 10.6.4 update could cause your disc drive to not accept previously readable discs for a number of reasons. When Snow Leopard was first released many users reported that the sensitivity of the OS to dust and scratches was extremely high, causing many users grief when attempting to rip music, load files, or install applications.
One thing you might check, especially if the disc is not one you burned yourself, is the format. When the disc shows up in Finder, highlight it and press (Command + i) to "Get Info." Check the format listed in the "General" section. If it is CD Audio, you should be able to read it. File formats that may not be readable include HFS, HFS+, or ISO9660.
Should this issue present itself, test the disc on another computer (Mac or PC) to be sure it works properly. Check the disc for excessive dust or scratches and clean if needed. If everything checks out, try logging in to or creating a new user account on your Mac and attempt to access the disc. One post claims that simply inserting and ejecting the disc in question several times may work (though you should be extremely careful if you're going to attempt that).
Though a specific fix for this issue does not appear to be available, we will keep an eye on this issue as users continue to experiment with solutions. For now, try running Disk Utility (Applications > Utilities) and Verify/Repair Permissions. You might also try a more robust system checking tool like the excellent (and still free) Onyx. We'll also keep an eye on developer builds of the next update to Snow Leopard to see if they will put any attention toward the problem.
Have you experienced this issue? Solved it? Let us know in the comments!