What can I do about my yard?

Late last summer and early this spring I had mole trouble where the moles burrowed right through my yard up against the sidewalk. Now instead of a nice gr edge, there's mounds of dirt all along the sidewalk. The drought we've been experiencing hasn't been helping. I water my gr all the time but the gr that is dying is only emphasizing the ugly dirt that the mole left behind. I also must note that the area is mostly in shade with mottled sunlight and the mole is now gone. I was planning on plugging my yard early in the fall with Zoysia and possibly sodding along the sidewalk. Does anyone else have any solutions to bring back that nice gr edge that I used to have?