Why is dark matter diffuse? Shouldn't it clump together? I guess if there's no Coulomb force the stuff just moves past itself. However there should be some kind of collision cross-section shouldn't there? Since there's so much of it, what would be the result of even a small probability of collision?
That's a very good question. The current 'best candidate' model predicts dark matter to be collisionless, i.e. the particles do not (often) collide with each other [1]. In other words, considering a 2-body system, the dark matter particles would accelerate towards each other, and then shoot straight past and decelerate on the other side, continuing to oscillate.
In that paradigm, considering a bulk of dark matter particles, the particles will be attracted to each other, and will fall towards the center of mass of the clump -- but there's nothing to stop them, and so they pass out to the other side of the cloud, where they decelerate. This puts a limit on how dense the cloud can become (I haven't studied the details of the mechanics here, but look into the Virial Theorem if you want the equations that describe these limits). In a normal cloud of gas in space, the particles would collide with something as they fall into the center of the cloud, which would convert their linear motion into random motion, and so they would essentially be trapped.
Note that while dark matter doesn't form dense objects, it does clump to some extent, and this is actually involved in galaxy formation [2]; based on initial small perturbations in the densities of matter before the inflationary period, the Cold Dark Matter forms clumps (halos) which act as the initial seeds of attraction for the baryonic matter (H/He) that formed the first galaxies.
