I am a noob to Med but it's obviously a UV skin map issue. Not really program specific. You need to make sure that your uv's are evenly distributed over the texture and mesh. Automatic skinning rarely works too great, you need to go in and hand tweak the UV cords in the skin editor to prevent texture stretching, you don't want to do atlas mapping if you are trying to wrap a texture seamlessly around a shape like that because there will be those problems at the seams usually.
Try looking up uv mapping (the technical term for skinning) on Google, it will give you the basics. It isn't something program specific but it is something that relates to texturing any 3d object in any program.
basicly, you need to make sure that nothing overlaps or is squashed in the wire view of the skin editor, try moving the points around in there and watch the results.
Hope it helps you some, UV mapping is one of the things most people have a lot of trouble with when first getting into texturing their 3D models.