I’m not sure I understand what the problem is.

What are your Brush settings anyway?

And you tried converting to 16 bit mode and re-painting as Noel suggested in other post?

Your display profile might be faulty, I guess.

Does turning off »Use Graphics Processor« in the Performance Preferences and restarting Photoshop have any bearing on the issue?

I think we should consider the conversation about your problem here, R.S., as Caroline's problem seems to have to do with brushing color into her documents, vs. the display of documents.

Could you please open this image into Photoshop, grab the screen, then apply a severe curves adjustment to spread the captured levels out so they're easily seen?

When I open the image into Photoshop 13.0.1 or 13.1.2, capture the screen, then enhance the image as I have described, it looks like this:

-Noel

No, the display of information with posterization, while it looks similar, really has nothing to do with the depositing of posterized data inside a document with a brush.  It's possible Caroline has your problem as well, which is further confusing matters.  Whether you have her problem remains to be seen.  Do something similar to what she did and post a copy of the 16 bit PNG file here.  I or others can verify whether the file has posterization in it.

By the way, if you're seeing the problem in not just Photoshop, how is reinstalling Photoshop going to help?

You might have a bad profile set up to describe your monitor...  Sometimes Windows updates bring in bad profiles. 

Or you might have a video card problem.  You seem to have eliminated the monitor.

Any chance you've managed to get your display set to 16 bit colors mode (sometimes called "High Color" mode)?  That's outdated as pretty much everyone uses 16 million colors, but many drivers still support it.

-Noel

The test image looks to have been rendered fine, the concentric rings are nice and even.

Now that you see the rings very plainly shown, when you look at the original dim gray version (without enhancement) do the rings look as evenly spaced as what you're seeing in the enhanced view?

-Noel

Assuming you're not just seeing the normal slight visibility of posterization on a good monitor showing 24 bit color, I believe you must be seeing something that others don't ONLY ON YOUR DISPLAY.  It's clearly not coming through in your screen grabs, which don't show anything wrong.  You're apparently looking at your own screen grabs with the same monitor and thinking you've captured the problem.

Your Curves-enhanced Windows background just shows the normal level transitions you see in 8 bits/channel imagery and whatever artifacts the image preparers left in the image.  I see the same thing when I do roughly the same Curves operation you did to the Windows 8 desktop background. There is no indication of a problem in this whatsoever.

There is no systemic problem - though you may have a problem with your specific system.  As has already been said, you most likely a problem with your video card or monitor. You need to replace things until it works right.

Only other thing I can suggest to further get folks to understand what you're really seeing, since the screenshots are doing nothing, is taking a high quality photograph of what you're actually seeing on your monitor.

-Noel

1.  Set your brush spacing smaller to paint more smoothly.

2 & 3:  It proves nothiing to show the posterization in an 8 bits/channel image that's been brought out by extreme enhancement using a strong Curves operation.  Everyone sees that.  This is why if you need to do extreme operations on image data it's suggested you work in 16 bits/channel.

-Noel

Brush Spacing is not measured in pixels.

-Noel

Are you actually SETTING your brush Spacing and Hardness?

-Noel