New Scientist put out an article on the mysteries surrounding gravity on their online site. I have included a snippet below.
SEVEN MYSTERIES OF GRAVITY
It's the force we all know about and think we understand. It keeps our feet firmly on the ground and our world circling the sun.
Yet look a little closer, and the certainties start to float away, revealing gravity as the most puzzling and least understood of the four fundamental forces of nature.
You can read them in detail here.
Questions are included in the article this go round (no reason to reinvent the wheel).