This solution only works when you have only a few songs in a playlist. If you have a playlist with a couple of hundred songs, this solution is simply not achievable, because I can’t find that specific song in such a big playlist.
Just mentioning, with the new update, there is now a way to delete a song from a playlist on the IPhone. Select the playlist, touch the words "and more" to see the full list of songs, then for that song, hit the ... button. it has four options, including "Remove from this playlist".
Did you try again today? I just did on my Galaxy s7 and there is a new option on each individual track. You don't have to find it in the massive playlist. You can delete the song that is currently playing from the playlist. This is what I wanted.
If you have your iPod set to automatically sync with your iTunes library, then just right-click the song you wish to remove and click "delete" (and click "move to recycling bin" after). Of it goes into cyberspace. If you don't want to permanently delete songs from iPhone, then uncheck it.
If you have your iPod set to manually manage your music, then you will need to plug your iPod into your computer. Then click "Music" under the iPod icon on iTunes (there may be an arrow hiding all the divisions of your iPod, but click it so it faces downwards). When all your songs are displayed, do the same thing I said above. It will no longer be on your iPod, but it will still be on your iTunes.