I just signed up because I saw this post and I'm having the exact same problem. My game was working 100% fine before the Holiday Gift Download happened earlier today and now no matter what I've tried I can't get a save file to load manually.
I've tried clearing my Xbox memory cache, deleted and reinstalled the entire game (including all save files), in order to start from scratch and after finishing the first mission Lamar and Franklin I tested to see if that had fixed it and it hasn't.
I've also tried to install the game disks onto a separate HDD to no avail. Same issue occurs. I'm pretty sure though that I've narrowed it down to something to do with online and being connected to Rockstar Social Club, as when I signed out of my profile and logged into another I was able to start the game from scratch and loading save files wasn't an issue.
I'm really hoping someone over at Rockstar can get this sorted soon. I was thoroughly enjoying the game experience until this happened. And I have now wasted half a day trying to trouble shoot the problem. And trust me, I've tried everything I could think of on my end and it definitely isn't my console or game disk as like I said it works under a different profile not registered with Rockstar Social Club.
I've been reading all the issues people have been having since he introduction of online and it sickens me to think that Rockstar is more concerned with focusing on the online side of things before fixing the single player side which is what sold the game to the masses to begin with.
I have filed a report with Rockstar Support in the hopes that they are aware of the issue and can resolve it soon, until then I recommend everyone who wants to be able to load old saves disconnect from the internet until it is fixed as that should solve the problem.