Error logs play an important part in determining what is going on with your setup. Sometimes errors are surpressed from screen viewing, so the results are stored in a file. The system itself will write to an error log in the root folder. That is the first file you should check. The file is named error_log and has no extension. There may be other erro_log files created within subdirectories, so check there too. (wp-admin, wp-content and wp-includes)
Within these files you will find very specific incidences of errors generated across the system, including which files tripped the error. This is helpful in narrowing down what to fix.
Sometimes they can get quite large, especially if left unattended, so once you’ve taken care of the generated errors (or found out they are some variation of “normal”) you can delete or shorten the file.
If you are running MU on a cPanel server, you can also find an error log there. Usually it is at http://yourdomain.tld:2082/frontend/x/stats/errlog.html or similar.
Often I find repeated request for non-exisiting files from one IP address. This is almost always a spammer of some kind, so feel free to add their IP to your deny list. Do this by editing your htaccess file manually, not by using an htaccess manager within cPanel, because it will overwrite it.