A quick note to myself (and whoever is interested :-))
Markus Neteler mentioned on the GRASS user mailing list a new library that came out that extracts valid data from within an OpenStreetMap input file. It is from the developer of Spatialite, and can be downloaded from here.
There are various options to import your data in a PostGIS database. The OSM2postgresql script (for Linux) sets up a PostgreSQL / PostGIS server or database (optional), imports OSM data into it, process those data (including multi-polygons with holes) and proposes a classification. Check out http://wiki.openstreetmap.org/wiki/Osm2postgresql (where you can find links to some alternative solutions too).