Rebooting Exchange Server 2003

I'd write down every detail about my server hardware. I'd have a look at my computer mfg's website to check for caveats. I'd learn how to backup Exchange and Active Directory. I'd learn all the ways they use Exchange. calendar? public folders? web interface? pop3 interface? proxy? btw is this Small Business Server? if it is, make sure you do all your changes and configurations with the wizards, not manually, at least not until you are more familiar. CG IT is excellent at small business server.
then I'd set up another test Exchange box and a sample client or two and make it as much the same as the production box as I could. and I'd test my patches there first I'd practice restoring my Exchange backups there.
other things i'd want to understand: where are folks mail files/personal folders/archive files?
finally, i'd reexamine my conclusion my boss knows nothing. that is not going to work as a philosophy if you ask me. you guys need to become friendly. anyway, he knew enough to hire you , yes? he might also be aware that more than one service pack has caused servers to fail to reboot, to become very slow etc etc.

It's hard to get into all the specifics since many companies run different 3rd party solutions such as antivirus, anti-spam solutions etc that interact with exchange, but in general what I recommend is to learn which services are essential to run your exchange server so you can verify their status after the reboot. You should of course perform backups before applying patches and ideally test the patches on a test box before applying them in production, but this isn't always an option in a small company (though creating a virtual machine running exchange 2003 may be an option).

Of course you want to schedule the reboot outside working hours and have a plan for speedy recovery in case something should go wrong.

If you use any kind of special 3rd party software such as server fail-over etc you should consult the documentation for that software.