I did some testing on MultiSite and found several mutlisite bugs that I'll fix for the next release, but I couldn't reproduce the issue you mentioned.
I did some searching and found two common reasons for that error:
1) An incomplete upgrade - see http://wordpress.org/support/topic/fatal-error-call-to-undefined-function-wp_get_current_user-in-homexxxxx. Make sure you run the network-wide upgrade script after you upgraded.
2) A plugin tries to access user info too early. I don't see anywhere that my plugin is doing that, so I don't think that's the issue.
Can you disable the plugin and check to see if you still get the error? If you do, then it's probably an incomplete upgrade. If you do still get the error, then let me know if you're trying to do a network-wide activation of the plugin or just for a single site.