I am almost done with my clean-up near the chain-link fence around the edge of the property. I saw some sprouts on what I had already done yesterday and this morning hoed them down. In doing so, I unearthed tangles of roots, stems, and leaves that I had buried earlier. Removing the bulk of them, I smoothed the soil again and continued around the rest of the fence. There are still areas where the debris still needs to be removed, but this is the first time I went around the perimeter completely. It didn't take that much time, and when I mow later I will not need to approach the fence.
That is the main problem with chain-link -- the weeds are nearly impossible to control unless one uses herbicides. Using weed-whackers isn't feasible because the plastic line wraps itself up on the fence and breaks off quickly. There still is a place for herbicides -- one neighbor isn't good at keeping his yard.