Get clang-tidy working

[roblabla]

It'd be nice to get clang-tidy working with our codebase, so we can:

1. Benefit from its lints, which seem to sometimes point out real issues
2. Use it to enforce some convention on variable naming and whatnot.

Unfortunately, clang-tidy seems to really hate the Windows headers. Obviously the MSVC7.0 headers are incompatible with clang-tidy, but I had trouble making them work even with newer headers (like the latest Windows SDK ones).