LEASH LAW: My California city has a "leash law" and I was wondering if a dog owner who violates this law is potentially liable for any bite injuries caused by the dog?

Generally speaking, yes.

If a dog owner owner violates a leash law, and her dog attacks someone, then that person is still said to be "strictly liable" for the dog bite, under California law.  You do not have to prove negligence on part of the dog owner in order to have a dog bite case, you just have to prove the dog bite occurred and caused you bodily injury.