Hello,
Of course we've tested the avast! for Mac on the latest OS X Mountain Lion. Antivirus software occasionally have unpredictable interactions with other software installed on your Mac and a resulting crash my be a product of bugs in that other software. We constantly fix these issues on our side even if it's not our fault.
We are sorry for any troubles caused even remotely by our software. We'd be happy to hear a specific list of other software you use like system tools, firewalls etc. We'll try to simulate the behavior here and fix it, if possible.
Regards,
Jan