/var/lock/apache2 created with root:root ownership (apache2 can't create lock files in it)

Binary package hint: apache2

/etc/init.d/apache2 does:

case $1 in
        start)
                [ -f /etc/apache2/httpd.conf ] || touch /etc/apache2/httpd.conf
                [ -d /var/run/apache2 ] || mkdir -p /var/run/apache2
                [ -d /var/lock/apache2 ] || mkdir -p /var/lock/apache2
                #ssl_scache shouldn't be here if we're just starting up.
                [ -f /var/run/apache2/ssl_scache ] && rm -f /var/run/apache2/*ssl_scache*
                log_begin_msg "Starting web server (apache2)..."
                if $APACHE2CTL start; then
                        log_end_msg 0
                else
                        log_end_msg 1
                fi
        ;;

Since /etc/init.d/apache2 is start by root, mkdir -p will end up creating a directory that is owned by root. The file /etc/apache2/mods-available/dav_fs.conf contains:

DAVLockDB /var/lock/apache2/DAVLock

Since the directory /var/lock/apache2/ is owned by root, the module is unable create the lock file, and webdav does not work correctly (only allows reading).