You should pay attention to your curves, which aren't as smooth as they supposed to be. The length of each segment should vary smoothly, and avoid accidents, very visible on the egg.
For the first picture, your anti-aliasing is not that bad. However, you have a problem on the trail, which seems too large. It's caused be the fact you're using anti-aliasing both on the bottom and on the bottom. Moreover, the gradients are not very useful, especially because they are barely perceptible and because they create squares or rectangles inside on the shape, which is actually bad.
I tried (very quickly) to reshape your comet, correct anti-aliasing and add some anti-aliasing/ambient light to the moon. The result is not perfect at all, but I think it shows how to fade and give some dynamic to your comet.
