to turn off "repeat this song", go to the now playing screen and tap on the album art to bring up the song info if it's not already there, then tap the two arrows that are chasing each other until it's not glowing any more
Thanks to you all for answering my question before I asked it.
The picture AND the instructions were both a help; it took me a minute to actually read closely enough to "tap" on the album art to get the "repeat" icon to appear.