Finally worked this out. Could not understand why I could not shuffle a playlist on my iPad mini. This is how to do it. When playing a track from a playlist tap on the double arrow next to the small album art work, this will give you a full screen artwork. Just above the pause button there are two icons one is a shuffle icon (it is hard to see as I was trying to shuffle tracks when I was outside and could not see the icon due to sunlight). Tap on it and it lights up and then tracks shuffle from a playlist. Happy days no more listending to playlists in alphabetical order.
@kjm322 - Sounds like the web player, you are right it is pretty tricky to find. That feedback has been passed over to the web guys. ;)
@Caz59 - You can star an entire album on iPad by pressing the "+" icon at the top of the album page. There is no easy way to star an entire playlist or artist page I'm afraid.