Problems with dark matter

Warning:  Physics ahead.

Dark matter is postulated to solve the 'missing matter problem.'  That is the problem?  There's not enough observable matter in the universe to make the observed rotation of galaxies work.  You see, spiral galaxies spin as if they were pinwheels, with things furthest from the center moving fastest.  Or, if you prefer, as if the stars were dots painted onto a round sheet of plastic that was then spun about its center on a pin.

Stars shouldn't do that in real life.  All theories of gravity hold that stars in the center of a galaxy should move much more quickly than the stars half way out, which in turn rotate faster than the stars at the edge.  But this isn't what happens.  So, there must be a whole bunch of missing, invisible matter in a giant cloud around the galaxy, making the stars spin with the enormous total gravity.  Dark matter doesn't interact with regular matter at all except through gravity.  It may or may not react with itself in unknown ways, but we can't really know.

Except that this doesn't work.  Sure, it explains the problems, but it creates new ones.  If the dark matter is there, and it has gravity, should it be clumping together into larger and larger lumps?  Shouldn't there be dark matter stars and planets, acting darkly and suspiciously?  Shouldn't we see the effects of these clumps?  What happens when a dark black hole tears entire solar systems apart? 

We don't see any of that.  Apparently, dark matter also has some property that keeps it at the density of fog, never congealing or clumping at all.  Could dark matter have some sort of universal monopole property, where every particle is repelled by every other particle, even as they are attracted by gravity?  If the force were less than gravity, gravity would eventually overcome it, and dark foam would form, possibly like pumice.  If the repelling force is greater than the attraction of gravity, then we would expect the dark matter to be evenly spread everywhere, except where the extra attraction of normal matter might possibly gather together a slightly denser fog.  But this wouldn't be enough to count as the five-sixths of all matter that dark matter is supposed to be.

It's really quite simple.  If something is affected by gravity, then that something should form clumps.  Dark matter, as postulated, should forms clumps on a large scale, but not on a small scale.  No means for this distinction is postulated.  Alternately, dark matter objects do exist in profusion (5/6 of all matter, remember), but we have never seen their effects anywhere, because reasons.