I've been able to run AutoCAD 2007 as well as most other software's I need on Windows Vista without problems. There are some things needed to have it working and it might be some things I have not tried that does not work for you. If you just try to start AutoCAD Microsoft warns about "minor compatibility issues" but I have not found them so far. Running as Administrator solves a lot of compatibility problems with applications and that is the same with ADT 2007.
Autodesk will be announcing official details on Microsoft Windows Vista support for AutoCAD and AutoCAD LT in the next 2-4 weeks according to Shaan. So you might want to wait until then.
Run the installation as Administrator.
Run also the application as Administrator. Right click to do that or change the properties to have it run as Administrator.
It is also possible to run a program in compatibility mode for Windows XP (Service Pack 2).
You can also turn off User Account Control (UAC).
What is your trick to get applications running on Windows Vista?