Culture Shock is the only Sam & Max episode that doesn't currently activate correctly on Vista, and that will be fixed in the very near future. Episodes 2 and 3 should be just fine.
As far as I know you can't activate the game on your XP machine and then play it over a network on your Vista machine... but then again, I've never actually tried it. If you mapped the XP machine as a drive for the Vista machine? Maybe.
There's no problem activating on more than one computer at a time, so if you want to give that a try, don't worry about messing up your activations. Just make sure to download onto any machine you want it activated on using the methods described here