NASA Scraps Shuttle And Returns to Rockets
I should have added to my list of things we can't fix yet "adequate space collision defense shield". We could surely do that without sending humans into space.
But I don't agree with you about colonies. There is no particular reason why we more than any other lifeform especially deserves to survive as a species. However, the idea that a small number of us might preserve our genes by going to some other rock in case the Earth gets it seems to me like pure science fiction. The human race isn't just a collection of genes. It's civil societies and the artefacts they create, including ideas. Surely it's worth putting more effort into protecting those? A few people living in an artificial environment on Mars at huge expense is no substitute for New York, or Venice, or the English Lakes, or any of the other threatened places of the Earth. (FI, I'm thinking of the risk of destruction of NY by tsunami, not terrorism).
As for the other poster's comment that Nasa is 0.7% of federal budget, what proportion of R&D is it? In other words, what percentage of the best brains does it occupy on manned spaceflight? I'm suggesting scientific and engineering skills be focussed on the real problems.