Test failure for Multibit on Windows
The tests you mention are tests that drive the UI classes directly. They are a bit like robot tests and are a bit fiddly. If you don't run those specific tests you lose a bit of UI test coverage but no coverage of the deeper classes.

RE: the code being poorly documented: There are lots of Java doc comments, pretty much everywhere. You'll appreciate that the documentation effort has been much more on the end user side of things. MultiBit is a fairly typical MVC architecture, though of course it has accumulated a fair amount of cruft over time. Surprisingly code is almost always documented in line.