Since WordPress is stupid about limiting what kinds of files you can upload with no method of changing it other than installing yet-another-plugin™, there is a quick way to disable the checks entirely if you’re running your own server and are the only one allowed to upload. This fix is global to WordPress, so be very aware if you set this that anyone who is allowed to upload a file will be able to upload ANY file (within the file size limit, of course).
To disable the security check, edit wp-config.php and add the line:
define('ALLOW_UNFILTERED_UPLOADS', true);