Something odd happens with regards to MUC rooms. If you create a MUC room, and send someone else an invitation, the user is not able to join the MUC room if that user is on a remote Openfire node. Disabling the 'members only' configuration option for the MUC is a workaround for the problem.
Initial investigation by Gato revealed that the member variable that of the MUC isn't updated over the cluster. LocalMUCRoom#addMember seems to be the cause of the problems.