mesh doesn't follow armature correctly - bones outside the mesh I set up the armature and weight painted every bone and everything seemed to be fine but the mesh doesn't follow correctly. it moves, but not as expected. (it seems to move too little)

I tried to fix vertex groups manually. There  is just one Armature Modifier. 
I really don't get it :(

here is my blend file: http://sta.sh/0edcqulrf04
I think the problem is that your weights, give influence to the movement of that part of the mesh (an arm of the creature) to two different bones:



So, afaik, the end of the arm, being influenced by two different bones, is a "compromise" (or more properly a "blend") of the position of the two involved bones. 

I roughly tried to correct the weights of the first image:


and you see the mesh now behaves better, hopefully?

(btw the other arm of your model already has a similar setup and the mesh moves like expected)