Max Payne 3 ran on a cloud service I'm pretty sure. Never had problems with that game. Not sounding like a "fanboy", but to be fair Rockstar hasn't ever made a huge massively open game like this. My time playing GTA:O, I've only experienced two problems.
1. When I did the mandatory starter race I would walk up to the marker, pull out my phone and wait, 20 seconds later it will repeat the scene where that random guy pulls up to me to show off his car, then the game gets stuck loading forever. Been told to remake character in second slot and it would fix. I did that and it fixed.
2. Logged into the game and it asked me to choose character, went to that screen and my character was invisible/no stats, still showed name and money though. Was told to just reboot the game. Did that and it fixed.
Playing Xbox in the United States, always make sure the cloud is up before I play, and I save on a regular basis(Every hour or so, using the singleplayer option on player wheel).
Seems like most problems are being experienced by ps3 users. I'm too afraid to lose my progress so I won't be logging in until its confirmed its fixed. Everyone make sure you save regularly and make sure it saves before you log out!