You did a very good job. I bet those minor puckers would come out with some echo quilting of the background or a stipple. Ditto what has been said about stabilizer. The satin stitch is very formal, if you want a quick way of salvaging this, and, not just "salvaging this," but to give it more excitement, keep what you have done, and free-motion zig zag - not tight, actual zigs and zags, just inside of the satin stitch. This could be done with the same thread, or one just a shade different, or even another color. When you do this, you don't have to follow the first satin stitches exactly, just go for it. If you do this, it is very forgiving, whereas satin stitch is not.
Good job!