When I first ran into this problem (when iOS 7.0 came out) I went to the Apple Store to speak with a "Genius". Recreating the symptom took a few attempts but was able to demonstrate to the "Genius" of the problem.
His only conclusion was that it was a defective "scanner" (the glass) and was willing to give me a replacement (a refurbished unit). I declined since my iPhone 5 was less than a year old and it's only the "swipe to answer" that is having problems.
I didn't even bother going to Verizon as I would probably be given the same choice.
That said, all Apple needs to do, I feel, is to give us the ability to disable the "swipe to answer" .. this way for those that like the swipe to answer can keep it. For me (and what seems like a lot of people), please give us back the old "Accept/Decline" buttons!!