-Wunused-local-typedefs is a new warning flag of gcc-4.7, and it will enabled by -Wall since gcc-4.8 (not yet released). The fix is a big set of removals of unused typedefs (or comments, or moves, depending on the context).
No header in this sub-directory, but Face_badness.h, is documented. They are internal headers of the Mesh_2 packages, and should not be used. If you want to use some undocumented functionnality, please contact me (Laurent Rineau <laurent.rineau@ens.fr>) so that we can see if I can move some internal details to the documented interface.