Odds are, if you pass errors from modules you didn't write, you're leaking information to the user that they either won't understand, or they will understand, and can potentially use to exploit the system.

I'd recommend trapping all errors, and sending them to the error log, but sending a generic message to the user. (hopefully something more than 'something went wrong ... contact the system administrator'). You might trap and leave a different generic message in different sections of your code.

Depending on what the site's doing (and how locked down it is in the first place), I might hide a more useful error code/message in the source, but typically, the error page is a feedback form to alert the sysadmin -- they can leave contact information if they wish, but I can also poll for HTTP_USER_AGENT and the like, and ask them what they were doing at the time it gave them problems.

And I think it goes without saying -- if you're likely to error out due to database connections, don't track this in the database, and if you're likely to error out from writing files, don't write it to a log file w/out some other form of backup. Mail is usually good, so long as the partition w/ the mqueue doesn't fill up. (and you watch it to make sure mail's actually flowing)