When you add the Word document  to SharePoint, the custom  properties of
the document are available and will be synchronized on the upload or a
save. For example if you have a custom property called "City" then if
you create the same column in a document library, whatever value is in
the Word doc will be set on an upload or save to SharePoint.
Alternately, any custom properties  you create in the doclib are turned
into custom properties in any Word documents  added to that library  and
synchronization will occur. You can use these properties for grouping in
views for example. I have a fairly lengthy blog on the subject here:

weblogs.asp.net/.../267846.aspx

In my experience with this, if I set up a column in the Doclib with the
same name as a custom  property with a value already defined in the
document, I end up having to re-enter it manually into Sharepoint,
either when I upload it or when I save it. I was hoping to avoid this
additional step... or is there no way around it?

Again it depends on how you save it or upload it.

1. Create a doclib with a property called "Blort"
2. Create a new Word document  and add a custom  property called
"Blort"

Uploading the document through the upload facility will clear out the
value (because it presents the metadata screen before the upload of the
document and uses the values from the screen rather than the document).

Uploading the document through the Upload Multiple Files (Office 2003 on
the client needed to see/use this) will preserve the custom property in
the document and sync it with the Doclib. Uploading through a drag/drop,
copy/cut/paste operation into Explorer view will do the same.

One other caveat to add - the name of the column must not be a "reserved" name
for the automatic promotion to happen. Names like "Author", "Modified", etc.

I tried exactly the steps listed, and it did work just fine with a
property of type 'text'. However, trying the same thing with a date
value was not so successful. The name of that property was just a
nonsensical random word... Is this something you may have encountered
before?

Only text types are valid for synchronization. It was all in my blog.