Some things here might be spoilers, but only if you consider area names spoilers.
 
Okay, so I had been playing FFXIII for about 40 hours while having no trouble when it froze for the first time. I was at the tower in Pulse, before Oerba. I thought "Fuck! There goes three hours!" but I redid that bit, saving at every opportunity. Then, when I got to Oerba proper, it froze again while I was accessing a save point. So this game has frozen twice within 5 hours after 40 hours of play. I thought nothing of it, but then it froze again about thirty minutes later when I was walking around outside of battle. Then I came here.

After doing some research, I have discovered that  Final Fantasy XIII freezing is a thing. I have also discovered that the console subsequently bricking is also a thing. Currently my PS3(60GB) can recognize the disk, which is scratchless. So my question is, should I be worried? Should I just stop playing? I have seen the videos posted by RuneWalsh and while my situation is not identical, I'm afraid it may yet be. Thoughts? I'm at a loss here.

I played through to the end (about 60-70 hours) on the PS3 and it didn't freeze up once.  I don't see any reason to worry.

What FFXIII freezing thing?  This is my first time hearing about it, and never ran into it during my playthroughs.  Are your other games working fine?

I heard about FF13 murdering older PS3s too. Since you've already had issues, I'm not sure if I'd continue playing if I was you. I guess it depends on if you have the money to replace it if it breaks.

This is the first time something like this has happened for me. This article explains it, and it also has the video I mentioned. I have no cash for a replacement PS3, so it would really suck if this bricked it. I'll try again later, and if it freezes again then I'll put the game down.

Hmmm, i played the whole game and got the platinum without freezing once. Sorry this is happening to you :( But yeah, if it could brick your ps3 I would stop playing, its not that great of a game :P