Spinning a bullet uses gyroscopic force to help keep it from tumbling and keeps the pointed end pushing through the air. Same principle as putting spin on a thrown football. It helps keep it on course. If you were shooting a gun on the Moon, the trajectory would be whatever it was coming out the barrel. The bullet could be spinning like crazy, or shaped like a Yoda action figure, and it wouldn't make much, if any, difference.

There's no point in spinning an asteroid, unless it's a big one and you're trying for artificial gravity inside.

A spacecraft, like some orbiting communication satellites, is sometimes spun slowly to help it maintain a specific attitude. Some payloads are spun while ejecting off a rocket for the same reasons--you want it pointed a certain way when the operation is done. True especially if you have a kick stage you want to fire without having to do a lot of thruster corrections.