I have MCLA & I have brought all the game add ons since doing so I have had the following problems.....
Lag the car freezes for a second when I have travel great distances (its not my net it's also doing it in single player mode)
Complete freezes (the game crashes normally when Im changing my car or trying to join a game)
Tearing of the picture (this only seems to happen on bits of the new south central map)
The steering wheel stops turning (this normally happens when I've been driving in static cam then change to the drivers view)
I was just wondering if anyone else is having the same problems & if so if they have any possible solutions?
I get the steering wheel one and where the road doesn't draw in properly and my car starts sinking downwards sometimes.
Is it since you downloaded the add-on? If so then i'd delete the 'game data' and download again. Go to Game on the XMB and up to 'Game Data Utility' and look for MC:LA. This will delete the add-on and any updates, then re-downlaod them again either by going back to the Store (look for downloads) and by starting the game (for the updates).
I know it might sound a pain, and might not solve it, but 8/10 times it does and you dont loose your save game data either.
Hope this helps.
EDIT: Oh it sounds daft but is the disc clean? Might just need a wipe 1st?