I think the most important quality of a song is its resonance. By that I mean its quality of being able to strike a chord with a listener and make something happen for that person. To my mind, the quality, which marks out the best songwriters is the ability to "hear" the songs rather than to just make them up. We can all make up words and tunes till kingdom come, but our efforts may not move any other person. So although I agree with most of the previous remarks on other threads about the craft, I think that the very best have an instinct, which tells them what will connect with other people.
Now I look forward to a chance to pick up some wisdom from some of the many fine writers on Mudcat!