1. The explosion might affect the orbit of Earth, changing it's course.
2. No tides, animals (like turtles) would not act like now
3. Asteroids might smash into Earth.

Well, there would probably be tons of debris that would rain down on us, and kill alot of us, then the earths orbit would change severly(maybe quickly or little by little but it would change)....then we would eventually perish for good....enjoy

The moon is not likely to explode, but it is disappearing. The moon is in an open orbit, meaning it's traveling fast enough to escape Earth's gravity. Every year, it recedes about an inch and a half from us. I will find some articles about this phenomenon, and post their urls.
http://eclipse.gsfc.nasa.gov/SEhelp/ApolloLaser.html
www.theevolutionofman.org

If the moon would explode then;
1. The face of earth facing the moon's explosion will likely to be destroyed by the big blocks of moon.
2. no tides will then be created .
3. we will not get any light at night and it will be completely dark.

If we lost the moon, it wouldn't matter what the after effects would be, explosion or no explosion. The moon is essential for Life to exist on this planet. Without its gravitational pull to keep us in the orbit that we now have, climatic conditions would change so severely Earth would just become another lifeless planet orbiting Sol.

Interesting, but fanciful, question... Since the core of the moon is solid and cool, the instability of the moon is not coming from inside. Only an outside influence would cause it to reshape.

Since it cannot explode, nothing would happen.

To pursue "what ifs" is fine, but inconsequential if they're not viable options.