After replacing the back cover on my Nexus 4, the ability to read NFC tags has decreased significantly. I replaced the back cover of my Nexus 4 with an original(!) replacement because the glass had broken. Yes, the new back cover has NFC and I've confirmed that by scanning the tags I used even before the cover replacement. It does work, because the tags can be scanned, but it takes a lot of tries and often I have to give up.
I test NFC capability by holding a known valid NFC tag at the center of the phone's back, and if that doesn't trigger then I very slowly slide the tag around the back, and repeatedly remove/reapply the tag. All my tags are the "sticker" type, and they're placed on a wooden surface (not metal), so it's not a matter of material or thickness.
I don't think I did the cover replacement badly, because it does work occasionally. Is it possible that the replacement is a poorer quality than the first? What can cause this problem, and how can I determine & fix it?