Since it was pointed out to me that I’d missed this:
If it were in tiny clumps, you’d need a lot of them, and they’d form a sort of gray fog across the sky. If instead they were in large clumps (called “MACHOs”, for "MAssive Compact Halo Objects), they’d be much harder to notice, at least via their overall fogging effect. But you could still detect them through what’s called microlensing: Every so often, one such clump would pass between us and a star, and its gravitational field would slightly bend light around it, causing a focusing effect which would make the star appear to momentarily brighten in a particular way. Microlensing searches have been done, and have concluded that MACHOs can account for only a small fraction of the dark matter.
But there’s another problem with MACHOs: What are they made of? We have very good bounds on the total amount of baryons (protons and neutrons) in the Universe, based on the relative abundances of isotopes of the lightweight elements. And that’s also far short of the dark matter total. Since our familiar sort of matter gets almost all of its mass from protons and neutrons, there must be some other sort of matter making up the dark matter. And if that nonbaryonic dark matter stuff, whatever it is, interacts with the electromagnetic force, then why can’t we detect any of it in our particle-accelerator experiments?