80k hits per day isn't that many. Who cares if your log file is a few 100 megs, you can still handle it. I've dealt with packet logs that big before.
My feeling is that there is an error / notice which is happening before the beginning of the script, possibly due to (as you suggest) bad cookies. Try increasing the error level in php.ini to E_ALL and ensuring that your logs have timestamps (mine do).
Then once you have a timestamp for the error, you can correlate it with the packet log to identify the exact cause.
Of course, display_errors should normally be off in a production environment, as you don't want end-users seeing any PHP errors (it is normally sensible to have a PHP error handler show them a custom error page, but you can't set an error handler before the script starts).
Mark