Nginx – Not Logging PHP Errors

When accessing some PHP scripts on my website, I'm getting the dreaded 500 error message. I'd like to know what's wrong to fix it, but Nginx isn't logging any PHP errors in the log file I have specified. This is my server block:

server {
    listen 80;
    server_name localhost;
    access_log /home/whitey/sites/localhost/logs/access.log;
    error_log /home/whitey/sites/localhost/logs/error.log error;
    root /home/whitey/sites/localhost/htdocs;
    index index.html index.php /index.php;

    location / { 

    }

    location ~ \.php$ {
        fastcgi_pass unix:/tmp/phpfpm.sock;
        fastcgi_param SCRIPT_FILENAME  $document_root$fastcgi_script_name;
        include fastcgi_params;
    }

    location ~* \.(?:ico|css|js|gif|jpe?g|png)$ {
        expires max;
    }
}

Note that some PHP scripts work fine, and others don't. So there isn't a global problem with PHP, there's just something in these scripts that's causing Nginx to throw the 500 error.

How can I get to the bottom of this? The only thing in error.log is an error about favicon.ico not being found.