I can access the youtube Playlist with the default youtube application on an iOS device by tapping "More" then "Playlists", but how can I play those lists? When I tap on a playlist, it shows the list of videos included in it, and I can only play them individually one at a time. I want to play the whole list continuously. I don't connect my device (iPod Touch 4) to a computer, so I cannot use a solution that uses iTunes.
There is no way you could do that, I have that problem also. You could try to send YouTube a feature request, but I won't think they will do that as Google now owns YouTube and Google and Apple aren't exactly the best friends... But you coud try :)