Strictly speaking the 'around the sound' pass is only valid for a one-way bridge transfer (you're meant to use the Helsingor-Helsingborg ferry in the other direct). Not that they check. Of course, if you take the ferry, you get a 20% discount on prawn sandwiches, so if that doesn't encourage you to go significantly out your way, I don't know what will.

(Well, there's also the Louisiana museum in Humlebaek, which is one of my favourite museums in Europe...)

If you're starting in Copenhagen, I believe you can only buy the ticket from SJ (Swedish Railways) - they have a booth (relatively limited hours) in the main station.