Freemind looking OK on Ubuntu 12.10 with stock Unity desktop. I've just downloaded freeplane 1.2.20 from freeplane.org as the version in Ubuntu repos is 1.1.3. Looks nice with useful additions to the mind map. Seems to run OK with the same java and libraries as were installed for freemind.

Do you have other java based software installed? Does that look ok?

http://packages.ubuntu.com/quantal/freemind

Ubuntu repos show freemind depending on openjdk (or Oracle) and that has a font package shown as a dependency.