I replaced my hot water heater on Saturday and ran into an issue I've never dealt with before. I shut off the cold water inlet into the hot water heater, opened up the spigot to drain it, and opened up the hot water valve in the kitchen to let air into the system. It never emptied. I had to cut of the water to the whole house before it would empty. Somehow I've got cold water backing into the hot water system. Does anyone know how this is happening?

My guess is that one or more of my shower/tub valves is allowing the water to move across, but that's just a guess. How do I isolate the issue and fix it?