Subdividing has warped my mesh. Is there a way to clean up this mesh after adding other modifiers? I am trying to create an unusual ring in Blender 2.77. After using the subdivision surface modifier on my ring, I noticed the change affected the formation of the vertices, which appear to look like slight dents on the shank (inside of ring). I have lost my earlier files due to a fault in my portable hard drive therefore I cannot carry on working from a previous file. I can start from scratch, but I thought it is better to ask of any possible ways to fix my current file. Modifiers have been added before I noticed the mistake. I am sorry if this does not make much sense, I am still new to Blender and could not figure out this issue. Whatever I researched did not come up with relevant answers.

I have found a file which contains an older version of my ring. As you can see the shank edge has many tris. I have tried to make these quads, but that only repeats the problem. I am guessing this is the reason the shank edge has slight dents in the design. What is the best way to clean up this mesh?
No sure it's adequate in your case, but I'd go in Sclupt mode, select any brush (the standard inflate/deflate will do), set its strength to 0 so that the shape isn't changed, but turn Autosmooth to 0.1 or something like that.

You will then be able to smooth the geometry with the brush just where needed, without touching anything else.