When I first got my iPod 6th Generation Nano, the one that looks like this, everything went smoothly for a while. Suddenly (and probably after an iTunes update), none of my playlists would play in order. I tried everything I could think of--numbering tracks, playing recordings as "albums," making sure to "unshuffle"--but nothing worked. Finally (with the help of Michael) I found a solution, which I will share here.
Here's what I did to solve the problem.
I turned the "shake to shuffle" feature off. (You find this in "music" on the iPod). Then I went to "settings" and reset the iPod a few times.
Then I went into iTunes and did a right click on the playlist in question. I chose "Copy to Play Order." I did it with all my playlists, and synched my iPod. Everything seems to be fine now, but I have to re-do "Copy to Play Order" every time I use the button on the top of the iPod to reset it. The default seems to be set not to play playlists in order. Perhaps the programmers at iTunes can fix this one of these days.