Unfortunately, I don't believe the television has the option to shuffle or do playlists when connected to the dock. However, if you wanted to do that with the player, you could hook it up through headphones. But from what I'm able to find, the dock doesn't have that functionality.
I have noticed that when I select a Playlist or an Album to play on the Ipod through the HT-BD3252, it plays the songs in alphabetical order. The only way I can find to prevent this is to change the name of the songs so that they start with numbers corresponding to where in the album or playlist they should appear.
Is there a setting or something I am missing that could get the HT-BD3252 to play the songs in the order in which they appear on the playlist or album? This does not happen when I play it through headphones or a car adapter.