Whenever the insecure notice comes up, it's usually because someone has linked to off-site content -- like an image -- which is hosted on a unsecure server. As time goes by this is becoming rarer and rarer, but it can still happen.
In a situation where someone has posted an image on DU which is hosted on a unsecure server, your browser would show a warning that the page is not fully secure, because of that single image.
However, I'm not sure that's what's going on here. My browser is not showing this page as unsecure, and turning off the avatars shouldn't make any difference because they are all hosted on DU's secure servers, not on unsecure third-party servers.
Potentially the issue could be something related to your computer's/browser's configuration. It could also be related to the fact that we had to restore the whole site from a backup yesterday -- I would actually be slightly amazed if something *didn't* go a bit screwy after that.
I'll pass this along to Elad to see if he has any thoughts...