What Marion said. The first part, anyway, saved me the trouble of writing it out. To facilitate learning to play over particular chords in an interesting and jazzy manner, learn major scales in all possible inversions so you have the whole fingerboard covered.

I'd have to say that I feel there can be mistakes made when improvising. My definition of a mistake is based on the premise that you can play absolutely any note in any key, but your phrase has to have a beginning and and most important, an ending in context of the chord structure. So the weird notes can be great and make you look highly advanced, but that can't be the end of the phrase, and usually shouldn't be held for more than a half-beat or so. Also, it can be a mistake if it is not timed correctly to mesh with the rest of what's being played...

The phrase you are playing should end on a note (or notes) that is part of the chord being played or implied, and within that there is a choice of notes to set different moods--the 1st to resolve, the 5th to leave it set up to return to the 1st (as in, end of break, sing next verse) and things like the 7th to make it bluesy or one of my favorites, the diminished progression--which has a peculiar alchemy whereby it breaks most of the rules about righ and wrong notes, but you still need to know where you're going...

W-O