"An expert is a man who has made all the mistakes which can be made, in a narrow field." Niels Henrik David Bohr
This almost perfectly describes my experience getting PerformancePoint Server 2007 running in standalone mode on my Vista laptop. Should you ever find yourself in a similar position, please refer to the resources below.
First Nick Barclay has an excellent post on setting the correct Application Pool permissions.
Second, User Account Control will bite you. Your choices are disable it all together (and cause your IT support staff to suffer cerebral aneurysm). Alternatively, you can ensure the user executing any Dashboard Designer previews (and publishing) has access to the Preview directory. If you did a next, next, next install of PPS, this would be C:\Program Files\Microsoft Office PerformancePoint Server\3.0\Monitoring\Preview.
Here we go again with Vista UAC. If you have problems creating a new data connection, and you have opened your (local) db to the entire world. This is where you should look. There could be an issue with PPS actually granting members of the Administrators group, on Vista, access as Admin to the monitoring server.
You can verify your authorization by selecting Options from the Office menu and using the Connect button in the resulting dialog.