Thanks @Slimmons, please try your browser on the v1.3.0 test server at http://gitlab.mattermost.com/community (if you have a gitlab.com account it's just one-click to join).
If that renders properly, then it's not a browser issue, and perhaps a CSS file got corrupted. Try using the Upgrade Guide and instead of upgrading, in Step 1 iv) just download v1.3.0 to replace your current file and see if that solves things?
Mattermost is a compiled binary so it's really weird to see styling issues like this...