Unfortunately textures within shapes don't react to bones as predictable as points, especially not in extreme situations as the bending of an arm. This is reasonable: while a fill in a shape is just the same colour value, a texture in that place must effectively bend into itself, which is a hard thing to do and cannot be done with just the few points of the bounding shape.
If you want to put images into masks, you need to check "warp with bones" in the image tab. Do a test first, with just two bones, and see how the image reacts when being forced to fold in itself: it's a weird effect and normally not useful.
I recommend to break apart the limbs into smaller pieces, at least upper arm/ lower arm, maybe even an elbow patch. It will take some experimentation to get a nice result without losing too much flexibility.
Your style is a really nice one, maybe the shapes could do with a bit of shading, like the nose? I recommend you have a look at Yuri Norsteyn, especially his film "Hedgehog in the Fog"
http://www.youtube.com/watch%3Fv%3DoW0j ... 2Tu9P_oqHg. Done without any computer, it's a masterpiece in terms of how many parts a cut-out character can have.
Good work already. Please keep us updated about your progress!