Nevermind my question. I was able to solve the problem on my own.
For anyone else having this problem, here is the solution:
On your handheld, go to the Calendar.
Click on Menu -> Filter
Click on "More..."
Check off the categories you want shown on the calendar of your handheld.
It's still not the perfect solution, IMO, as, if I set up private appointments, I wouldn't necessarily want all employees to be able to turn on the appropriate filters and see what other employees are doing, but it will work. I don't really have to schedule too many private appointments anyway, so no big deal.
For my employees and myself, I have three different PDAs that I use to keep everyone's schedules current.
With two of the PDAs (an old Dell Axim, running Windows Mobile 2003 and a Samsung handheld running Windows Mobile 2003), I am able to select which "categories" I want to sync with each individual handheld.
However, when I open ActiveSync and try to go to "Settings" on the calendar, it only gives me the option to set how many weeks worth of appointments I want to sync. It doesn't give me the option to "Sync only events within the selected categories".
Does anyone know why it's not letting me choose the categories? I use the categories to differentiate between employees, and so, I only want to sync each employee's own events to that employee's handheld.
BTW - The one that's not working for me is a fairly new HP Ipaq running Windows Mobile Version 5.
I can't seem to find an "About" screen for ActiveSync on any of the handhelds, so I can't tell you which version of ActiveSync is on each one.
I am running 4.2.0 on my PC.