How do I best resolve PHP Fatal Errors?

I have increased my php.ini setting for max_execution_time to 60 seconds and memory_limit to 512M (which is a ridiculously high setting), but I'm still getting fatal errors on both:

- PHP Fatal error: Maximum execution time of 60 seconds exceeded in
/home/causeint/public_html/wp-includes/capabilities.php on line 749

- PHP Fatal error: Allowed memory size of 536870912 bytes exhausted (tried to
allocate 52654 bytes) in /home/causeint/public_html/wp-includes/functions.php on line 251

My website hosting company says that I need to find out why those php scripts are blowing the limits because it would be ridiculous to set them any higher.

So what would be the best approach to seeing what's causing the errors for each script? Do I run a trace, or something similar (I've never run a php trace before ... the last time I did one was with COBOL and Fortran, and you can guess how long ago that was)?

Thanks ... Michael