The reason is that the shapes will be all distorted. The moon should be somewhat roundly shaped, not a thin oval. >_>
Same goes with stretching 4:3 to 16:9, really.
In order to properly change ratio, you'd have to crop or letterbox/pillarbox.
The amount of detail also plays a role in this: for example, if you have a 720x480 input (standard DVD resolution), scaling it to 1280x720, even with the proper cropping, will most likely look bad. Of course, it's possible to upscale in a way that doesn't look like eyecancer, but upscaling is stupid since you're inflating the filesize for no detail gain. Chances are actually the upscale might come out looking worse than the original, especially if you try to go back to the original resolution.
As for improving quality, there's avisynth for that, but here's the thing: you don't use avisynth to magically improve quality, because it doesn't do that. You don't throw filters to the video and call it done, what you do is see what issues your video has, and try to fix them in a way that the output wouldn't have been better left unfiltered. For example, if you have some slight haloing, it might be best to leave it there, 'cause chances are fixing that will blur away more detail than the halo removal is worth.
You can find out about these things and more if you Read
ErMaC & AbsoluteDestiny's Friendly AMV Guides Lovingly Overhauled Largely by Zarxrax. There are specific sections that deal with them. Be aware that some things aren't quite optimal in the guide, but generally speaking the explanations are "good enough" for AMVer purposes.