It's not "continuous play mode," if you are referring to putting the power switch in the middle position. That is play-in-order mode.
When you turn ON the shuffle, you are playing songs from the All Songs list. When the power switch is set to play-in-order, the All Songs list DOES play in order. It plays in alphabetical order. It may seem like a random (shuffled) order, because you are not thinking about the song names.
If you have a playlist synced to the shuffle, and you want to that playlist in the list order you set up in iTunes, you need to use VoiceOver to switch to that playlist. This document explains how to enable and use VoiceOver to select a playlist that is loaded on the shuffle
http://support.apple.com/kb/ht4322
When you select a specific playlist, the songs will play in the list order seen in iTunes before you synced that playlist to the shuffle (when the power switch is set to play-in-order).