If it is not affecting your phone other than moving around a bit, I would just leave it. Replacing just the glass is near to impossible since it is heated onto the LCD. You could try buying a case that secures the phone together, that way you wont be letting dust and dirt in there.
I have the exact same problem. My phone also has grey/white blocks at the very bottom of the screen where I cannot touch. The keyboard problem makes texting so frustrating I hardly do anymore, unless I use Siri to write it for me. I had accidentally left plastic on the new screen, but just took that off and it still does it. Ive checked and reconnected the cables 4 times now, and nothing has fixed it. Unfortunately nobody has responded to your question...I'm just letting you know that you're not alone!