I had problems when adressing folders without trailing slash. Apache 2.0.40 (as server with mod_dav) returns 301 for accessing "/folder" instead of "/folder/". However, the webdav client lib did not call setFollowRedirect(true) on the HttpMethodBase. The real trouble is that while getting the childResources, the new URLs are build by appending the displayName to the base name, but without adding a trailing slash. (See WebdavResource.setWebdavProperties(Enumeration responses).) A workable solution for me was to put a setFollowRedirects(true) in all XMLResponseMethodBase constructors.
This will be fixed in the 2.1 release.