Sounds to me like the optical laser is giving out, or is for some reason having difficulties reading the discs. If there's some sort of lens cleaner for the PS3, that might be the first thing to try, otherwise you're probably looking at having to have the drive replaced.
It's been a little while since I've played Uncharted 3, so I don't recall whether or not it installs any game data on the HDD to cut down on loading times. I don't recall anything like that, and seem to recall Uncharted generally using some clever loading techniques to avoid that need, plus just taking the time to create a very polished product. If I'm wrong about that, then it's at least theoretically possible the HDD is going bad and causing problems, but my money would still be more on the bluray drive knowing as I do how frequently ODDs die.