You don't say what stitches you're using to stitch the edges of your applique. Mostly it just takes practice. And no matter how uneven and ugly you think your stitches are if you put it away for a couple of days and then look at it from normal viewing distance chances are you won't even be able to find the one or two misplaced stitches anymore.
I've used invisible thread with a straight stitch and a teeny zig zag, matching threads with a straight stitch and a blanket stitch, contrasting threads with straight and blanket stitches. I never use a satin stitch and I never use a stabilizer.