Black boxes and other weird behaviour in Photoshop

Since Photoshop CS6 was launched, and subsequently Photoshop CC, we've seen many complaints of weird visual behaviour of the interface.  Here are two scenarios, and possible fixes:

PROBLEM 1: BLACK BOXES ETC

Black boxes that appear and disappear randomly on your images, something like this:

Not only black boxes, though.  Sometimes white boxes, or weird blue colours in the Liquify screen, or image disappearing when you draw a crop marquee, etc.  Annoying stuff. Never problems with the image itself, just with the way it's displayed.

SOLUTION A:  Go to Edit>Preferences>Performance, and click on the "Advanced" button. Change the Drawing Mode to Basic, then restart Photoshop.  In fact, restart your whole computer if you haven't done so recently.

SOLUTION B:  If Solution A doesn't work, go back to Edit>Preferences>Performance, and uncheck the "Graphics Processor" checkbox to turn it off altogether, then restart Photoshop again.

PROBLEM 2: TERRIBLE GRAIN
When your photos look awfully grainy or noisy, but when you zoom in to 100% it goes away.

SOLUTION:  Go to Edit>Preferences>Performance, and check your Cache Levels.  You'll find they're on 1 or maybe 2.  Change them to 4, then restart Photoshop (or your whole computer if you haven't done so for a while):

DESPERATION:

If none of the above solutions work for your issue, fill this out then post the results in Ask Damien, along with a description of your issue, or better still a screenshot to demonstrate it.