I've been through two GNex's with these same issues...
1. it's picky about the chargers. Some chargers will charge it while others won't and the ones that won't charge it definitely work because they will charge other phones. It's very frustrating and I can't find a car charger that works!
2. weak 4G/3G reception. Other phones on VZW's network have at least double the signal strength when the phones are sitting directly next to each other. (not as annoying as the finicky charger thing but annoying none the less)
Just wondering if these are common occurrences or if I should be making a bigger fuss with VZW.
I'm currently running CM9 but this was happening on stock ROMS and other custom roms as well.
Thanks for your input.