Adding a new playlist to Spotify on the PC almost instantly added it to our iPhone list, too. Completely dynamic and very responsive.
The updating was similarly superb for adding new tracks to the playlists. All are kept in sync rather nicely.
Clicking Offline playlists at the top of the screen takes you through to this screen, enabling you to select which playlist to take offline (note the warning message saying they need Wi-Fi to download, so you can't download a batch of tracks over 3G).
Then going back to the main playlist screen, you can see them queuing to download.
After enabling Wi-Fi, the tracks start to download automatically. We'd be very, very interested to know in what format the tracks are downloaded and stored, while the number of tracks you can download may be limited we guess – perhaps even by Apple.
Clicking on the specific playlist takes you to this screen, where you can shuffle or play a specific track, as well as edit the list.
Switching on Airplane Mode turns the app blue, with non-synched playlists greyed out and synched ones available to play.
Here's Bruce playing offline. Oh, and if you quit the app when it's playing (probably because you want to do something else temporarily) it will start playing from where you left off.