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Just to clarify, with a bumper you can still use NFC and wireless charging, correct?
Yes. I have used Google wallet with the bumper on and see no reason why wireless charging would not work.
The wireless charging though ... since it's an electromagnetic field, the "inverse-square law" still applies, so manufacturers have used "resonant inductive coupling" to counteract the i-sl and improve efficiency between the sending and receiving coils, the primary limiting factor being the coil diameters in both components of the system.

My auxiliary cord is pretty thin at the end, and it still won't work with this bumper. There's only about a millimeter of extra space for the cord grip. I find it hard to believe that any cord could work with it, given the poor design.You mentioned in your review that it took a little extra effort to get your auxiliary cord to seat all the way. I had this problem with my last case as the auxiliary cord going in to my car stereo is pretty fat at the end. It didn't matter too much b/c my car dock wouldn't work w/ my case on but it was a PITA to keep taking off the case every time I wanted to dock the phone and I ended up hardly ever using it. Won't make that mistake again. Any dock I get is going to have to work with the bumper on and I'm hoping my auxiliary cord will fit or I can modify the size of the hole w/o making it look awful.
My auxiliary cord is pretty thin at the end, and it still won't work with this bumper. There's only about a millimeter of extra space for the cord grip. I find it hard to believe that any cord could work with it, given the poor design.
I have no problems with my charging cord either. Im actually still using my old blackberry charging cord. Fits fine with the bumper.
Actually, we are talking about the auxillary headphone port.
So the Nexus 4 is available for order again and the people who were on backorder are getting their phones this week (me included), however the bumpers are still on backorder. I ordered mine on the 13th and never got an email or update about it. It still says pending in Google Wallet and on Google Play they are still listed as sold out.
Now I can understand a phone taking a while to get caught up because of all the technology inside, but how hard is it to manufacture a rubber bumper?