The cold water is dripping in my sink and I just changed the replacement cartridge but it is still dripping. What else could be wrong?

Did you grease the cartridge with plumbers silicone before installing? Installation Help / Animated Tutorials for Moen Faucet (http://www.moen.com/consumer-support/installation-help/tutorial?id=moen0133) That helps but there may also be a scratch in the valve body, had any trouble getting the old one out?