There are features like "Edge Enhancement" and "Motion Smoothing" that supposedly work hand-in-hand to improve the image, but I'm not particularly convinced that they succeed all that well, except on the roughest images.

Edge Enhancement is pretty much what you are talking about with audio.

The way I applied it to audio, was to treat the spectral analyzer output as an image. Where the weird artifacts showed up most was when the overtones weren't precisely edited the same way. It was especially obvious in stereo, where weird glitches were really obvious hard-left or hard-right because of differences in the smoothing. Even if you couldn't identify what happened, it would catch your attention one side or the other. And it took away a lot of the "alive-ness" which I described as making guitar sound more synthy.

Here's the type of image I was working with: http://www.music-software-reviews.com/image-files/adobe_audi...

This was back in the latter 90's / early Y2K, so there might be significantly better methods available for keeping it consistent now.