“Is there a way to see that polys are overlapping but not connected?”
That’ll be mostly a matter of switching to Edit Mode and looking really hard. Changing display Modes,switch between Wireframe and Solid. Between Vertex/Edge/Face Select. Moving things around. You will learn about most available tricks.
But, in your case, I would first check the Normals. Inconsistent Normals can really mess up your Subsurf.
