I can see the shuffle indicator at the lower right of the Album artwork. When I "press it" it turns ever so slightly darker in hue while pressing, but when I lift off it returns exactly the same as before and does not "bold". There is no change at all. And the shuffle icon does not change the state displayed in the "controls" pulldown. No box or any indicator appears to confirm it's a will produce an action.

When you think of all the millions of lines of code its a miracle it works at all. I guess that's it. It just doesn't work. But it does jump songs, so it's doing something - incidentally an action I did not ask for. I want it to shuffle or not. I did not poke a "change song" button. The stuff doesn't work, yet they release it anyway.
Thanks ed2345 for your observation that yours 'highlights' and is visible.
But to confirm shuffle is "ON" you still have to cycle the button to observe both states of boldness. Why must I be alert to watch for a change of state? It should clearly inform if shuffle is active or not at a glance, and not have to "remember subtle hints" or search a forum to use the software. Apple was not so sloppy years back. The stuff just worked, the user interface was elegant. No need to ask how to use it. And the forums were not so full of exasperated users wondering why Apple software is getting so hard to use. That shuffle (or NOT) requires a forum query, is a travesty in GUI design. Do they even read the forums?
Yep on the iPhone its even worse. I can't get it off shuffle. And whats worse, songs disappear off the album list. That app is really a lost cause, I'm always afraid to update IOS for the loss of usability thats become inevitable. I used the iPhone podcast apps years ago and really enjoyed it, but the app is so exasperating now I have quit listening to podcasts. But its attractive, minimalist.
Thanks for your help ed, but I think it's another example how Apple has lost their way.