Apparently it's not possible to load the list of branches and tags if the repository is opened under a custom URL. As long as the URL contains the bitbucket.org URL, everything works fine. If it's something else, it doesn't work.
For instance try to open the branches and tags list on the source tab for the following repositories:
- http://hg.secondlife.com/viewer-development -> Doesn't work
- https://bitbucket.org/lindenlab/viewer-development -> Same repo as above, does work
Or another example: