Debug Intermittent 500 Internal Server error & 404 Not Found

I have an intermittent 500 backend server error problem. The error sometimes appears when refreshing on the 2nd or 3rd page and sometimes it doesn't appear for hours and then suddenly a popup appears. I also noticed that I am getting intermittent 404 not found errors in some files. Apache error_log returns no errors and I am wondering if this is a coding issue. If this is an encoding problem, why would it be intermittent and why am I getting random 404 errors for files that exist?

What steps does SO recommend for detecting and debugging such a situation? Anyone have any ideas on what might go wrong?

Also, I am not pushing any process constraint (s) and these errors are exclusive to JS (.php) files.

Any help / advice is appreciated!