Recently I downloaded some hair and in some windows on the CAS menu it just shows the nude body of a sim, the CC still works. Though when you click on it in the clothing section the male's body will disappear and the female will have a random outfit placed on her.

This is what you get when the game lacks part of the download - the mesh or the texture. This is most often because the missing element was not included in the download (if, for example, the outfit is "repositoried" to another outfit you don't have), because it corrupted during download, or because it's being interfered with by something that uses the same mesh. Go back to wear you got the download and reread the download text, check to see if any special instructions or links are provided that you overlooked the first time.

If I'm misunderstanding you and sims can dress in the clothing and look all right, and it's only the thumbnail that's messed up, try CTRL+Right Click to update the thumbnails. You may or may not need the testingcheats on for this to work.