I know what the problem is, it's the mesh, not the texture. For the lightbeams, it looks like edges were simply extruded from the eye and mouth holes, resulting in kind of a mess.
So what you have is multiple, overlapping transparent polys. A lot of game engines have a problem determining the "draw order" in this scenario, it isn't a FPSC unique problem. The shockwave 3d engine suffers the same problem. If you look at the "wormholes" in your model, they occur in the places where the lightbeams fold back over each other.
That is why volumetric shafts of light in games are usually contructed of a single plane, or perhaps a cone. If you use a cone, you can move all the way around it without having any overlapping forward-facing polys. Your polys in the pumpkin are like paper folding back over itself. My searchlight from Model Pack 2 uses a cone to simulate volumetric lighting.
If I were you I would replace the light shafts with single planes to simulate the light shafts, it'll look cleaner and you shouldn't have any draw order problems from most angles. You might get away with using cones, but I would think that planes would do the job nicely.
