The safest thing is have some clean virtual machine, on which you can test your program. On every version you'd like to test, restore the VM to its initial clean value. Then install your program using its setup, and see if it works.
Dll problems have different faces. If you use Visual Studio and dynamically link to the CRT, you have to distribute the CRT DLLs. Update your VS, and you have to distribute another version of the CRT. Just checking dependencies is not enough, as you might miss those. Doing a full install on a clean machine is the only safe solution, IMO.
If you don't want to setup a full-blown test environment and have Windows 7, you can use XP-Mode as the initial clean machine, and XP-More to duplicate the VM.