I had supercache running very well on a large multisite install (12,000+ blogs)
When I upgraded to WP 3.4.1, and subsequently upgraded supercache, it is no longer working.
I've completely wiped out the cache and re-installed the plugin, but when I enable the cache, the first blog that gets cached is served on all blogs.
Inside the /wp-content/cache/supercache/ directory is only a single folder "mydomain.com"
The first blog that gets cached gets cached in that folder, and that cached file is served for all blogs, so the wrong cache is being served.
Before the upgrade, every blog had its own folder within the /supercache/ directory. So it appears that supercache is not reading the full blog URL (subdomain blogs).
This is running on Ubuntu 12.04 + nginx +php-fpm. The only thing that changed was upgrading to WP 3.4.1 and the latest version of super cache.