We correct downturned corners of the mouth with filler and have great results. This procedure really makes a huge difference in overall appearance, and often we have a good amount of product left to correct other lines in the face.
I agree with the other doctors on this thread that Botox injections in the DAO muscle at the corner of the mouth can make a very noticeable improvement in downturned mouth corners. Caution must be used in this area, however, to avoid a crooked smile appearance. I also routinely place fillers such as Restylane or Juvederm in this area for best results. Good luck