The sqlite3 database file files.db ought to be located in /var/lib/minidlna AFAIK. There was a copy of that file in that location, but when I took a look at its contents using sqliteman, I could see that the data in the database were very outdated. Media which had been deleted were still indexed in the database and newly added media were not indexed at all. So, I stopped the minidlna daemon, deleated the files.db file, and restarted minidlna (as sudo) with the -R argument to rescan the media files.
Everything is working fine, but there is no sign of files.db having been recreated in the /var/lib/minidlna directory. In fact, there is no sign of files.db anywhere in the filesystem.
The log says:
[2013/04/02 11:22:15] minidlna.c:884: warn: Starting MiniDLNA version 1.0.25 [SQLite 3.7.9].
[2013/04/02 11:22:15] minidlna.c:907: warn: Creating new database...
[2013/04/02 11:22:15] minidlna.c:990: warn: HTTP listening on port 8200
[2013/04/02 11:22:15] scanner.c:731: warn: Scanning /home/ray/Music
[2013/04/02 11:22:16] scanner.c:802: warn: Scanning /home/ray/Music finished (28 files)!
[2013/04/02 11:22:16] playlist.c:125: warn: Parsing playlists...
SOLVED: I had uncommented the line in mindlna.conf which selects the directory (/var/cache/minidlna) where the database and art_cache are stored. Strangely, although files.db existed in that directory, it was not found when searching for it from the Linux Mint menu.