You can create a directory for the playlists and the error logs that is not in /var/. I use /usr/share/mpd for mine, which is the default on Gentoo.
Code:
port "6600"
music_directory "/mnt/temp/music"
playlist_directory "/usr/share/mpd/playlists"
log_file "/usr/share/mpd/mpd.log"
error_file "/usr/share/mpd/error.log"
user "mpd"
That's what my mpd.conf looks like. The logging doesn't go through syslog, so it isn't that big of a problem. The only issue I had was making it so that mpd could access the sound devices. I definitely wouldn't run mpd on a multiuser box that has ssh access from people who may enjoy playing pranks. Heh.