Of New Scientist's (02 September 2009 ) list of "13 more things that don't make sense" by Michael Brooks, here, a surprising number relate to cosmology - 7 of 13.
They are, in order of make-senselessness,
1. Axis of evil: Radiation left from the big bang is still glowing in the sky – in a mysterious and controversial pattern
2. Dark flow: Something unseeable and far bigger than anything in the known universe is hauling a group of galaxies towards it at inexplicable speed
4. Fly-by anomalies: Space probes using Earth's gravity to get a slingshot speed boost are moving faster than they should. Call in dark matter
8. Antimatter mystery: The big bang should have created matter and antimatter in equal amounts – so why didn't the universe disappear in a puff of self-annihilation?
9. The lithium problem: The universe only contains a third as much lithium as it's supposed to
10. MAGIC results: High-energy radiation from a gamma-ray burst reached Earth 4 minutes later than the lower-energy rays. That's not how Einstein said it would be
12. Noise from the edge of the universe
New Scientist is a fun read, but based on its treatment of subjects I know a bit about, like non-materialist neuroscience, I wouldn't take it too seriously. Still, these anomalies really are anomalies - at least. Maybe harbingers of big discoveries to come?