I apologize if this has been dealt with elsewhere. I searched and didn't see it anywhere else.
I sync my iPad with iTunes on my computer, so it ends up with all the same music. But when I'm using my iPad, I can't get onto iTunes unless there's an internet connection. (Right? Is that normal? Seems silly to me, if I only want to use it to play my music and not to shop.) So I end up just clicking on the "Music" app that's automatically on the iPad, and play my music from there. It has all the same music, but my custom playlists get rearranged with the songs out of order. (Though it plays normal albums in the right order.)
Am I doing something really stupid? Because it certainly seems like one of Apple's own products with a built-in music app should be able to play an iTunes playlist correctly. My ancient iPod certainly plays playlists in the correct order.