I took a look at the md3 model.
My first thought was that maybe you had duplicated faces leading to some kind of
z-fighting effect, but that doesn't seem to be the case. I tried using W - 6 (remove duplicated), but there were no duplicated verts to remove. I grabbed random verts and dragged them around in case there were faces close enough to cause z-fighting without actually having duplicated vertices, but every time I moved a vertex there was nothing being left behind, so it's not z-fighting.
The fact that it shows up in the correct place when it's visible implies there is nothing wrong with the model's origin point, but I imported the tremulous blaster for comparison anyway. They had the same model origin and lined up pretty well location wise, so there's no problem there.
I'm really not sure what your problem is, but I can't see anything wrong with your model.