Here's a good advice: enable PHP logging, and take a close look to it. I found this error message for every webdav request sent:
PHP Fatal error: Call to undefined function mysql_real_escape_string() in /var/www/ezpublish-4.0.0/lib/ezdb/classes/ezmysqldb
.php on line 908
The solution is simple, just install the php-mysql package.
I hope this saves you some time :-)