Here is an odd problem I encounter from time to time. I will do a Dynamesh of a subtool and go back to smoothing, but instead of smoothing, I get these strange artifacts. Some times I can close out of ZBrush, and reopen the file and all is well. Other times even that does not work and I am stuck. Any clues as to what causes this?
The opposite of smoothen is roughen or rough up. Alt and Zsub do the opposite thing in ZBrush. So, don’t use Alt with Shift or don’t use Zsub. Instead, use Zadd with Shift to smoothen.
Hi zber2!
That is exactly what I am doing. I am using Shift with Zadd. That is what is confusing about the results. I can be going just fine, and then all of a sudden it starts doing it again. In the screen shot, you can see I have Zadd selected. Beyond that, the only other thing I am doing is using the Shift key (which I believe shows up in the attached image as the Smoothing tool being selected up in the top left).
I think I stumbled on the problem. I am using a tablet and pen. I have not set the pen buttons to anything in particular for ZBrush, but apparently if I accidentally bump into one of the buttons occasionally, as I twist the pen around between my fingers, I reverse the current mode. I just need to reclick the button and I am back in business
Details, details! 
Glad your all sorted. Cheers! 
You as well! Thanks for your help!