When I click on a contact I can see, General, Detail, Activities,
Certificates and All fields, but I'm not seeing any categories unless I
select "All contact fields" under the All Fields tab

Make sure the contact window is tall enough to show the Categories and Contacts controls, which appear at the very bottom.

I can display category assignments of contacts in "By Category" view but I
don't seem able to view categories in the "Address Cards" view.

Modify the view to add the Categories field.
--
Sue Mosher, Outlook MVP
Author of Configuring Microsoft Outlook 2003
http://www.turtleflock.com/olconfig/index.htm
and Microsoft Outlook Programming - Jumpstart for
Administrators, Power Users, and Developers
http://www.outlookcode.com/jumpstart.aspx