Unfortunately this doesn't have anything to do with the FlexUnit code itself. These are bugs inside of the Flash Builder plugin. You may want to post on their forum as well to try to get some support.
The only advice I can offer, is that things seem to work much better if I consistently use the Execute FlexUnit Tests, which can be found under the run button. They work much less well if I right click and tell it to execute tests.
I actually managed to get this working.
I had to copy flexunitextended.swc and FlexUnitTestRunner_rb.swc to my lib folder.
Understood, but for future reference if you do use the Execute Flex Unit tests from the run menu like I mentioned. That function seems to understand it needs to copy those files, whereas the right click version seems to assume they are already there.