I just spent the last day trying to help a friend diagnose their Mac problems. They had tried upgrading their Mac Mini to Mountain Lion and the install process got hung half way through, objecting to the hard drive.
Somehow the hard drive became corrupted and the install process asked whether we wanted to choose another disk, get help, or try the Disk Utility to repair the drive. But even if we chose the repair option, it wouldn't let us repair the hard drive.
The next thing to try would have been to boot off the SuperDrive and try and repair the hard drive, except that the internal SuperDrive had stopped working a few months ago. I thought about buying an external SuperDrive, but when I did a Google search and the consensus seemed to be that you can't boot from external SuperDrives.
Then I discovered this article: Make a bootable USB flash drive to run & repair Mac OS X | MacYourself.
I thought that sounded like a great idea, and went and bought a 32GB flash drive. BIG MISTAKE. The installation took forever, and then the machine ran like it was in super sold molasses...it was virtually impossible to do anything, it took so long for any task to complete. After several hours of going through the install process and trying to get Disk Utility to work, we gave up.
And then I had a brainstorm...why not use a regular external hard harddrive? And why didn't I just do that in the first instance? I have no clear answer...I guess I just got wrapped up in the first solution.
Fortunately, after taking out the USB Flash drive, attaching an external hard drive and rebooting, the Mac came back at the beginning of the install process, and let us install the OS onto the new hard drive. It even let us run the Migration Assistant and copy files from the internal hard drive to the external. Interestingly, the internal still seems to work; the OS install just doesn't like it.
Things seem to be okay at the moment....we just have to figure out whether we can reformat the internal drive and copy everything back to it....but we'll try that next week.