iPhone 5s Touch Screen Issues

This is my first post on The Verge. I just recently bought two iPhone 5s, one for myself and one for the wife. What we immediately noticed is that the touch screen on the 5s is unresponsive along the right edge of the screen. You have to press multiple times for a touch to register.

This is evident when pressing the p key, delete, return and trying to go to a particular alphabet in our contacts. At first I thought that it was a problem with just my 5s and I thought that I may have gotten a faulty unit. But then my wife complained of the exact same issue and I didn't understand how two brand new phones could suffer from the same issue.

Are there any other 5s owners facing the same issue? Have we gotten faulty units in which case we should get them replaced or is this a known bug on the 5s?