Moon: Grass blocks or Saplings do not grow in moonlight, however they won't decay in moonlight either. 
The moon illuminates topmost blocks during the night in the same way that the sun illuminates them in the day, but only illuminates them to a Light level of four, rather than the sun's fifteen. 
Phases of the Moon: In Minecraft Beta 1.9 Pre-release 4, the Moon goes through eight lunar phases.[1][2] The phases are: Full Moon, Waning Gibbous, Last Quarter, Waning Crescent, New Moon, Waxing Crescent, First Quarter, Waxing Gibbous. This would allow the player to keep track of the passage of time via the Lunar calendar after Beta 1.9 Pre-release 4. A full cycle of all eight phases is equal to one Lunar month or Lunation. Twelve lunations is equal to one lunar year. 
Mobs: Hostile Mobs will spawn around dark areas of a normally generated map. When the moon is up, hostile Skeleton, Creeper, Zombie, Endermen and Spider mobs will appear and attack the player. When the sun comes back up Skeleton and Zombies will burn in the sunlight and drop items after death. Spiders will not burn in daylight, but instead become neutral during the day, only to become hostile again if attacked, when it is night, or when it falls into a dark area. Endermen will not burn in daylight, but instead become neutral during the day, only to become hostile again if attacked or looked upon, but will instantly teleport away and become neutral again if the Player approaches them. Creeper and Slime mobs do not burn, and will remain hostile during the day
Stars: Together with the moon, the night sky also consists of stars. The stars look like little white squares and are an overlay over the Void that rotates as the night progresses. 
Trivia: Night time lasts 7 minutes, plus 1.5 minutes each of sunrising and sunsetting. 
The Moon and Sun are not visible while using the Short or Tiny render distance settings. 
The moon is 8 x 8 pixels. 
In past versions, there was a stars file in the game files, but at some point it was replaced with seed generated stars. They are now unique to the given seed of the map. 
According to Notch, the Minecraft sun and moon actually rose in the north, not in the east.[4] This was a bug, but was left in the game.[5] This was changed in Minecraft Beta 1.9 Pre-release 4, so the sun and moon now rise in the east.[6] 
In Beta 1.9 Pre-release 4, one can find out on which hemisphere his/hers Minecraft world is by studying the moon phases (see gallery). The hemisphere that the world is on seems to be chosen randomly and stays the same, no matter how far the player goes. 
In Minecraft Beta 1.9 Pre-release 6, the Sun and Moon textures were reverted back to their square form. The Moon Phases were redone in a square shape. 
The Moon is rotated 90 degrees. It appears to be lit from a source in the north or south, whereas it should be lit from the east or west. 
The Minecraft Moon progresses in the Sky relative to the sun. Earth's Moon does not do this, which is why it can be seen during the day. 
Minecraft cannot have eclipses due to the above. 
Notch stated back in February 21st, 2010 that he might consider allowing the player to travel to the Moon, similarly to traveling to The Nether.[7] The likelihood of this seems diminished as of this point, however, considering the incorporation into the phases introduced. 