I have a black and white wire for a thermostat instalation. I'm put the black wire to R, and the White to W.
New thermostat is on a Hot water heating system for the condo, and I have reprogramed to as such.
New thermostat is a RTH7400/RTH7500. We have replaced the zone valve and the unit is still calling for heat.

Do I have the wires hoocked up properly, or should I move the black to AUX, and keep the white on the W?

You have the wires hooked up correctly, but, unhook the wires at the stat and see if the boiler is still getting a call for heat. If it is, unhook the wires at the boiler or zone valve and see if boiler still runs. What you are doing here is eliminating the stat and stat wiring to see if one of them is the problem.