If you watch Bruce Almighty before, there is a part where Bruce (Jim Carrey) pull the moon nearer to earth, and eventually make a mess of our earth climate.

Contrary, if the moon is removed, we would not have experience the monthly tide change. Ocean tide is extremely important not only to sea creature, but also create a cascading effect in energy circulation. Due to lack of water rise and fall, water current will become relatively calm. Warm place will become warmer, while cold place will become colder. Eventually, due to high differential in climate across region, will cause huge pressure differential. During season change, we are likely to experience more hostile weather.