I started using the REST API Browser and noticed that many of the commands do not give me a chance to fill in some of the "template" parameters, such as /rest/api/1.0/projects/{projectkey}/repos/{repositorySlug}/branches
For that page there is no place to enter the two template variables above, but there is plenty for parameters passed on the query string.
Compare with /rest/api/1.0/projects/{projectkey}/repos/{repositorySlug}, which has the two necessary parameters.
The problem appears to be the application.wadl file (http://bitbucket.dtex.lan:7990/rest/api/1.0/application.wadl). The problematic methods are missing the param elements for the template variables (style="template").
Tried raising this as a bug but the ticking system directed me here.... I think :)