Could someone point me in the right direction to see in the SMC / NS Console a list of all currently connected agents? I'm sure I've seen it before but can't find it anywhere...

See this IDEA

https://www-secure.symantec.com/connect/ideas/altiris-agent-statusactiveinactive-console-dashboard

OK, so is there any other way to see what clients are still connecting to a particular server? A filter on the logs or anything? We're trying to decommission one server having moved the clients to another, so want to see if anything is still pointing to the old

See this thread

Need to report ONLY active assets (Computers)

https://www-secure.symantec.com/connect/forums/need-report-only-active-assets-computers

How does an asset's Status work?

Look at Reports > Notification Server Management > Agent > Agent Requests.