I figured this one out via this post on Mitch Denny's blog.  To be able to install the Web Application Projects add-in for Visual Studio 2005 on Windows Vista Beta 2 or 5536 you need to run the installer as an administrator. 

The easiest way to do this is to hit the windows key, type command, right-click on Command Prompt at the top of the list, and select Run as administrator.  This will launch the command prompt, then all you have to do is run the installer from this command window and the administrator privileges will be granted to the WAP installer.

As a side note, I am loving Vista's instant search that occurs when you hit the windows key.  I have been using it as an application launcher for the last couple of days.