Some applications have grey menu bar When running (for example) a java application (Minecraft) in it's own space (in Mavericks) the menu bar disappears, but then a grey bar appears on top of the space.

Is there anyway to fix this? It happens in Eclipse as well. Immediately after giving it its own space it's fine, but after the screen saver or sleep mode (I am unsure what set of events causes the problem in Eclipse) it shows up.
Not entirely sure but Mavericks introduced a menu bar on all screens. It may be that these programs are not aware of this feature. EG they need an update for this to be fixed. Check the forums for this manufacturer.