I also have this error in 4.5.3. The URL /wp-admin/admin-ajax.php is returning a 404 in the admin screens, for example in Appearance->Themes->Add New->Featured.
I have checked file permissions and that the file is actually present and I get the following response:
Date: Wed, 13 Jul 2016 21:22:59 GMT
Server: lighttpd/1.4.39
X-Powered-By: PHP/7.0.7
Transfer-Encoding: chunked
Content-type: text/html; charset=UTF-8
404 Not Found
I did have to set define(‘CONCATENATE_SCRIPTS’, false); in wp-config to fix another issue, so I wonder if this is related (removing CONCATENATE_SCRIPTS makes the admin screens practically unusable).
I’m *very* new to WP so any help gratefully received!