I'm almost embarrassed to post this: I can't re-order the songs in any playlists on my Mac. It's iTunes 12.1.0.50 on OSX Yosemite 10.10.2.
The playlists are all sorted in manual order. There doesn't appear to be anything wrong with them. They all play; each playlist, each song. It is a mixture of playlists I've created on this computer and ones I've synced from another. They are not shuffled. iTunes Match is enabled and not currently syncing. I've quit and restarted iTunes.
Just in case I've missed something, here's a screenshot:
Help me Ask Different, you're my only hope.
Best Answer
posted as answer to add pic…
This tells me it's shuffled right now; click it to turn off again.
Re-ordering should be as simple as dragging to a new position, but whilst it's shuffled it will appear to ignore you, as it's unlikely to recalculate the shuffle at that point.