.NET Extensibility is a Windows Feature (on Vista & 2008) that must be enabled/installed/turned-on before BDJX can be hooked into IIS 7.
The BDJX 7.1 Installer (and Admin Console) will attempt to install/enable .NET Extensibility for you if it detects that it is not present when installing an IIS 7 Adapter/Handler.
However in some cases it will be unable to do so.
In that case you must enable .NET Extensibility yourself.
Here is how to turn it on in Vista:
Control Panel - Programs & Features - Turn Windows features on or off - Internet Imformation Services - World Wide Web Services - Application Development Features - .NET Extensibility
Check the checkbox to turn it on. Then try again to install the BDJX 7.1 IIS 7 adapter via the BD Admin Console.