Thanks to Julien (of MacManiak) for having told us about this problem.
In order to ensure compatibility with iTunes and to allow music streaming in the iTunes app from a NAS server, most (if not all) of the manufacturers of these devices (Netgear, Synology, QNap, ...) use the open-source Firefly Media Server software. In iTunes 10 playlists on the server are visible, but the actual media files are inaccessible.
Without warning anyone, Apple has broken compatibility with this open source software, depriving all owners of this type of device, and there are many, from having remote access to their centralised music store. A thread about this topic on Apple Discussions iTunes 10 breaks Firefly Media Server / mt-daapd has been closed. Some other discussions without real solutions are currently active on both the Netgear and Synology forums.
Currently, the only way to regain this functionality under OS X requires a reinstallation of iTunes 9 which is complicated, very complicated.
Let's hope that this is only an oversight or an unfortunate error on the part of Apple and that they will reverse their mistake. Otherwise, it will be necessary to find another solution, FireFly being no longer under active development.
[Update] Thanks again to Julien for this new information:
NETGEAR is on the case and will include fixes in their next updates (for ReadyNAS SPARC, ReadyNAS x86 and Stora). Meanwhile, Vince has written a plugin which changes certain settings in FireFly so that it no longer upsets the much-loved iTunes 10:
http://www.readynas.com/forum/viewtopic.php?p=256850#p256850
For the moment, it's only available for the NETGEAR x86-based NAS systems.
