The way it works for me is this:

First I come up with a sketch of the proof and try to formalise it and find holes in it. This is fairly creative and free and fun. After a while I go away feeling great that I might have proven the result.

The next day or so, fear starts to creep in and I go back to the proof with a fresh mind and try to break it in as many ways as possible. What is motivating me is that I know that if I show somebody this half baked proof it's quite likely that they will point out a major flaw it. That would be really embarrassing. Thus, I imagine that it's somebody else's proof and my job is to show why it's broken.

After a while of my trying to break it, I'll then show it to somebody kind who won't laugh at me if it's wrong, but is pretty careful at checking these things. Then another person... slowly my fear of having screwed up lifts. Then I'm ready to submit to publish.

So in short: I'm motivated to get proofs right (I have yet to have a published proof corrected, not counting blog posts) out of a fear of looking bad. What motivates me to publish at all is the feeling for satisfaction that I draw from the achievement. In my moderate experience of mathematicians, they often seem to have similar emotional forces at work.