After an installation of Team Foundation Server you might want to customize the Team Site that has been created for you. If you add a Web Part to a page you will receive the following error:
"An unexpected error has occurred"
After a bit of searching I found a Microsoft Support Article which described the exact error/scenario we were experiencing.
I contacted Microsoft and obtained the post-Service Pack 2 hotfix package for Microsoft Windows SharePoint Services and installed it and restarted the web server. We are now able to add Web Parts.