I guess that's the wierd part.  In this example, all I did was add a new field.

My suspicion is that the issue is versioning and content types.  Can someone
give me a high level overview of the process for changing a form template
properly / versioning once it's already been published? (an administrator
approved template)

My assumption is:
1)  Form designer has copy saved locally, they publish to my library.  
They're forced by the wizard to save the form to be approved.  (we save them
to a network share)
2)  The MOSS administrator approves the template in central administration,
and activates it to a site collection.
3)  Someone with appropriate permissions makes the approved content type the
"default" content type in the doc/form library, and sets the option to render
in browser
-At this point, we have v1 of the form running.  Next:
4.) To change the template (say, add a field), we can either a) open the
template on the network share and make changes, then re-publish (using the
same name), and go through the approval process again to properly version the
form, or b) do the same thing, but do it by opening the "pre-published"
(locally saved) copy of the form, overwriting the template on the network
share when publishing.

Is this right?  If this is done properly, changes to a form should not
require any changes in the doc/form library, right? (because there's only one
content type there).

I suspect our issues arose when we published v2 of the form, but gave it a
new name (thus making it a new content type available in the library).

Gavin, to answer your question, they don't get an error, they are just
prompted to open the form in infopath (client)...which works fine if they
have infopath installed.