Lots of 500.shtml page not found errors in logs
The 500 error page is show when the server has an internal error.  

Your server is looking for a file named 500.shtml because a directive set that as the page that must be shown when the server has an internal error. The .htaccess file used by Drupal set the page for the "page not found" error to /index.php with the directive ErrorDocument, but it doesn't set any error page for any 500 codes, which is the set by the server using a different file; for Apache, this means the access.conf file, or any files included by that file.

For what can cause an internal error, it could be a server directive, or a wrong argument passed to such directives. Other causes could be:


directory permissions
file permissions
a wrong transfer mode used when transferring the Drupal PHP files to the remote server when using FTP
the line endings of the files that don't match the one used from the Operating System that is hosting the server