Goofs

When Bugs Bunny takes off in a space rocket heading for the moon, he tries to open the escape hatch. This would prove to be a fatal mistake as Bugs Bunny would be sucked out of the rocket caused by the vacuum effect which would result in losing oxygen as there's no air in space and it would kill Bugs Bunny.

When Bugs Bunny crash lands on the moon, he opens the door and exits out of the rocket without his spacesuit. This would prove to be a fatal mistake. Since astronauts need to wear a spacesuit with oxygen tank, they also need to have their heater on to warm them up when it gets extremely cold on the moon. Since Bugs Bunny isn't wearing his spacesuit, he would suffocate, freeze to death, his body would explode and die since he doesn't have protection against the harsh elements of the moon, and no oxygen since it doesn't have trees and plants or life forms living on the moon.

If Bugs Bunny was up in space inside the rocket, he would be floating around weightlessly due to escaping the earths gravity and his supply of carrots would also float around the room.

If Bugs Bunny walked on the moon, he would weigh 6 times less than on Earth, he would be able to bounce around on the moon, this is due to the moons gravity being much lighter than Earths gravity. Since it shows Bugs Bunny walking, he would bounce a lot. Also, after the moon gets blown up. Bugs Bunny, Marvin the Martian and his alien dog wouldn't be hanging on for dear life, but they would actually float around helplessly in space.

The rocket ship is shown being loaded with hundreds of carrots for Bugs Bunny yet when Bugs is shown inside the rocket ship there are no carrots anywhere.

After the moon gets blown up by Bugs Bunny, Marvin the Martin and his alien dog is seen hanging on the crescent part of the moon. If the moon blew up. Then the oceans waves would no longer move and calm down which would affect life in the ocean. Also the moon pieces would form around Earth like Saturn, earth would be in danger of getting hit by meteor showers as the moon protects Earth from meteor showers. There would no longer be a moon eclipse, the length of the day would remain constant, the axial tilt would be unstable and earth would eventually freeze ushering in the ice age.