Not saying this is the exact issue you're having, but I did encounter a similar problem with my OG Droid. I bought a cheap replacement digitizer off eBay for an issue exactly like yours. When I installed it, the problem was actually worse than before the replacement. I bought one from a better reviewed manufacturer on Amazon and it worked like a charm. So I would say there's definitely a chance that you just got a bad replacement. They do seem to be somewhat fragile by nature.
Galaxy Nexus - Daily Driver - Paranoid Android 3.50 Alpha (05/12 build)
Sony Xperia Play - GrooveIP WiFi home phone / Gaming Device - Rooted Stock GB
Droid Charge - In-car music device - Tweaked 3.2 / Lazarus Recharged Kernel
Kindle Fire - Hashcode Stock JB 4.2.2 / Hashcode kernel
Asus EeePC 900 - Dual-Boot Android x86 4.0 ICS RC1 / Ubuntu Linux
Retired: Droid Incredible 2, OG Droid, OG Droid #2