Without knowing much about how you went about modeling, rigging and animating this character I can only take wild stabs at where its went wrong, but maybe this will help.
I am guessing that at some point you scaled this after animating and it also looks like the verts aren't welded resulting in these being thrown around when you export the model to .x.
Go back to Max and remove the skin modifier from the mesh, go into vertex mode and select all, weld it with a setting of 0.01 distance.
Now apply reset xform, collapse the modifier stack, now re-apply a skin modifier and tweak the envelopes to suit.
If you have more than one modifier in the stack then collapse it down, .x will only retain info from the first modifier at export.
It also looks similar to an issue sometimes seen with bone weighted shaders so if you have one applied in that view....you could try removing it
I don't trip over...I do random gravity checks.