I do not believe this is related to a video driver. I can reproduce this bug consistently, and I have the latest drivers from AMD.
Placing a painting only crashes the game if you are using a custom resource pack (any custom resource pack). If you are using the default resource pack, then you can place paintings without error. Apply any custom resource pack (I've tried five different ones of varying resolution), try to place a painting, and the game crashes to the desktop.
Perhaps there was a change to the painting logic that isn't being handled properly by the custom resource packs? Resource pack authors would need to know about it in order to fix their resource packs.
I did some testing with 13w41a and this issue appears to be resolved in that snapshot. I was able to place new paintings, log into a single player map with new paintings applied, and log into a multiplayer map with new paintings applied without any crashes. I've logged in and out of both games several times with no problems.