The avast! BSOD is very rare. I am providing avast! tech support to over 4000 organizations world wide. I earned avast! Rising Star 2010. Here is what I have learned on this subject:
I have cured avast! BSODs by using CCleaner registry tool. CCleaner should be run multiple times until it comes up clean. This may also be the last step, so keep reading.
A/V software is the most invasive application you will ever have on your computer. Many times there are leftover pieces of A/V software that cause conflicts (including avast!) I get very aggressive here by scouring the system for these. Look in Program Files for any directories of previous A/V programs. Get their removal tools and use them. Do the same for avast! (if avast!, run the removal tool for every version of avast! that has ever been installed)
Last statement is: removal tools still leave registry entries. So I use CCleaner, or manual registry hacks when needed.
Hopes this helps!
J.R. Guthrie
President at Advantage Micro Corporation
Failure Analysis Engineer