Can screenprotectors affect touchscreen functionality on the iPad 4th gen?

I have a brand new iPad 4th gen and had a Zagg Invisishield screen protector put onto it. I want to know if that can cause touchscreen issues. I have found there are dead spots on the touchscreen and also at times, phantom touching happening as well. I don't want to remove the screen protector until I know for sure because it was a little pricey.