I decided to follow some ideas of @colosimo to get rid of the effects of HDR on the moving moon and clouds. I like that this moon is more clear but I'm not sure about the dark shadow around it. Instead of using bracketed shots and sending them through HDR, I used two different shots- the clouds from one, the moon from another and cut and pasted. What do you think?
I see what you mean about the dark shadow... you may have been using a brush with feathering. If you're in photoshop, right click when you have the brush selected and adjust the hardness to 90% or so... then you can zoom in and be more precise about only coping the moon and not the area immediately surrounding it.