For whatever reason, rotating multiple compex objects using CTRL-M will cause 100's of Erroneous "Invalid" errors!
The actual reason is as following:
Surfaces must be planar, that is, completely flat. Programming-wise, grid locations are integers (0, 1, 2, etc), not floats (0.5, 2.0, etc). As a result, rotating brushes may cause vertices to go off the grid. In the editor, that's fine, seemingly they're treated as floats there. But the compilers will cast these to integers, causing some (usually minor) differences, often enough to make surfaces not completely planar. That's where errors start popping up.
So, I would advise not to stick to degrees as a valuable measurement. Personally I don't really stick to precise and exact placement of objects anymore, as it often results in over-tidy, too clean feeling maps. In real-life, not everything matches precisely, not everything is rotated perfectly or constructed exactly to the millimeter. Take some care with the technical aspects for performance and workability reasons, but don't limit yourself with artificial rules like tidyness. Of course, sometimes there's a place for these, some map themes require tidy placement, but keep in mind it's just a rule that you should break when you need to.
Edit: there's another kind of overlap consisting of simultaneous brush faces occupying the same place in the map. This should of course be avoided!
It's called z-fighting, two surfaces 'fighting' to be drawn first. May also happen on large distances, when the distance between each other is relatively small compared to their distance to you. Not a pretty sight indeed.