It looks partially like a normal problem (try recalculating your normals) but mostly like it’s too close and a bit too dense to have much beneficial effect.
Here’s the original Pixar paper that MeshDeform was created from. You can check the screenshots and diagrams inside to get a better feel for how it was meant to be used.
EDIT: Another thing it could be is a couple vertices JUST MISSING the inside of the meshdeform mesh, in which case increasing the distance between the shoulder meshdeform vertices and the model could fix the problem anyway.
I fixed the problem with putting in some more edges and moving the vertices away from the object.
If it was really necessary to put in more edges? I’m not shure, but it does not hurt (you wrote about vertices that “miss” the mesh).
I’m afraid that I haven’t understood the thing behind the mesh-deforming. Since some weeks I am trying around with several deform meshes and mixed armature / MD rigging. And there are still some questions open.
That document is really interesting. Hope it gives me some answers.
Actually the document there is mostly technical jargon, but the very interesting part I thought was that you saw the exact deform meshes that Pixar used for rigging Remy (from Ratatouille) and Dash (from The Incredibles), excellent resource information, and a very good insight as to how many vertices are generally used, and what shape the mesh should be. I might personally revamp the mesh you were using there, if it was up to me, but it seems fine the way it is now, and I don’t know how much time or effort you have left for it, so it’s up to you.
Another interesting thing you’ll see if you look into the document is how they use it for rigging faces. Using meshes INSIDE meshes and stuff, to isolate facial features and squash-and-stretch things like eyes without having any rotation problems.
Anyway, if you do have any more questions, feel free to ask away, if I can answer them I will, and if there are plenty of other people on the forum who can pick up your questions. That’s what community is for.