Limpy, by David T. Rorvik

This book is about a boy who is handicapped. He is numb on his left side from birth. He is not paralyzed. The book starts when he is eight. He hangs out with a group of boys around his age. They go on adventures and do things that boys of that age do. The boys accept their friend as he is and think nothing of his handicap.
There’s a three-lagged dog that wonders into town, a stray, a really motley looking mutt. Everyone chases it off. This handicapped boy takes the dog in and befriends him. He names the dog Limpy.
Limpy starts going on adventures with the boys, but the town’s people don’t like the mutt. Something has been turning over trash cans and getting into things at night in town and the people know it’s the three-legged dog. They want it destroyed.