When you click the
!-in-a-triangle icon, does the popup you see look something like this?
If so, the problem is that all the chat rooms are full of user avatars, site icons and other display content loaded over insecure HTTP. This is not quite as serious an issue as e.g. insecure scripts would be, and so Firefox does not block such images by default, but it does show a warning icon.
Fortunately, if you don't like the idea of loading images insecurely, there's a way to fix this:
about:config into the Firefox address bar, and click past the "Are you sure?" dialog that comes up.
Find the config key named
security.mixed_content.block_display_content and set its value to true.
The first two steps will get rid of the insecure content warning, but you'll see a lot of broken images, so the last step is to install either the HTTPS Everywhere extension or the SOUP user script to fix them.
(Alas, the HTTPS image fix included in the current stable version (v1.16.0) of SOUP does not fully support chat. I just checked in some improved code to the development branch that should fix this, but it hasn't been extensively tested yet. I'll need to decide if I'm confident enough in my code to push it to the stable branch today, because if not, the next opportunity will be in two weeks.)
Ps. Related feature request: Make all i.stack.imgur.com links protocol-relative