Update -- 5:30 PM ET 10/3/13:
We're currently working on a title update for both PlayStation 3 and Xbox 360 to address commonly reported issues with GTA Online. We hope to have it out for download as soon as tomorrow.
If you are still having issues with GTA Online and would like to be notified of updates, you can subscribe to this Rockstar Support article.
UPDATED 4:00PM ET: The title update is now available for PS3, the one for Xbox is coming soon.
Update -- 4AM ET 10/5/13: The latest title update for GTA Online is live for Xbox 360.