This has sat untouched for a while, so I did a quick search and found this article which sums it up nicely. They key factors with regard to earth science would be: 1) Less extreme tides. The tides would only be linked to the sun and would not be as strong. They would also peak at noon. read more
Beside of providing a beautiful view, moon also plays an important role in earth’s significant characteristics . Here are some things which will happen if moon is removed - 1. read more
The greater concern would be in the long-term, regarding the Earth's wobbling spin axis. Right now the spin axis of the Earth very slowly wobbles over 26,000 years, like a slowing wobbling top, because of the tug of the sun. The wobble causes true north to not always point at Polaris, a.k.a., the North Star. read more