I got BF3 when it came out and have not yet been able to play it without it constantly crashing. I have messed with all the settings, both in game and directly on the GPU. The one thing I found that might help me, setting the base clock speed to 100 MHz (I hear default is 133 MHz), I cannot do because my BIOS does not appear to have an option for it. I'm pretty sure it's a graphics issue, perhaps with the memory overloading, because when I put the settings low I can play longer, but restarting the game immediately crashes it immediately.
My computer is a Dell but I upgraded it with the PS and GPU. The BIOS is Aptio. Everything is brand new.
You might not need my help but, I had the same issues. I raised the core voltage to 1.00v from the stock like .967 or something. I was able to run the game with my GPU overclocked to 900Mhz with 0 issues. I used MSI afterburner for the settings.