Offline messages and little icons

Its not exactly push notification -- which will likely never be in sworim because its not connecting to the server through a proxy -- however if you xmpp server supports offline messages (such as google talk)  then you will receive them when you open the application.
On the improved UI front,  there's a notification badge added to the chat tab when new messages come in showing the number of unread messages.

Clicking on he blue arrow near a buddys name on the right will also show a detail  page for that buddy so its possible to read longer status messages