MacOS Mojave stacks not grouping by type

There are a couple clues here that indicate this is a software corruption of the graphics buffers and not a hardware issue.

1. The issue corrects immediately after a reboot
2. The issue doesn’t affect the entire screen
3. The issue affects layers of image and not the overall picture

Since the graphics architecture of macOS is that each layer of an image is allocated memory and then the software determines if a specific button or frame or windows is on screen and then if it’s visible on screen (whether minimized and visible as a thumbnail or if it’s not obscured by an element more front most than it) the corruption shown is either blanking or fuzzing the bits in one layer.

Hardware errors tend to get worse with time (often rapidly deteriorating) and the hardware doesn’t get cooler or somehow fix itself when the OS reloads. Yes the drivers are restarted and hardware might power down most of the units briefly as part of a restart, but in general it’s the same Mac after the restart as it was before.

Now, none of that helps immediately.

The next time you get this corruption, I would open system preferences and make a new account. Log out of your current account that has the glitches and see if the glitches happen when you log in to the new account. If so, you know the glitches are either hardware or corruption in the base system. That’s good since you can either reinstall the OS or get hardware repair.

If logging in to the new user is clean - no issues. Log out of the new user and back in to your old user - not restarting the OS yet.

If the log in to the old user is glitchy - you need to isolate the software causes (update the OS, update your apps, clean your settings) or just reboot more often. If the old user is not glitchy, you have the least actionable case - it’s some corruption that happens rarely or by chance and “fixing” it will be hard if it’s not a system bug that Apple eventually fixes.

Good luck, keep your backups current in case you get tired of this and choose to erase the OS entirely, reinstall a new OS and then move your data and apps back from the backup.

I went through almost exactly what you went through. I fully reinstall Mojave with no luck, so just downloaded the Media Key Forwarder (note: it's no longer called Media Key Enabler). I recommend it until Apple fixes their 'unified play'/'Now playing' mess.

Update

Boot into safe mode (hold shift as you press the power button, or click here for instructions). Start iTunes and the play buttons should work, then reboot normally and enjoy life.