I spoke to soon it just died today, won't do a thing had 60% battery too, light won't even come on when charging. Lucky i bought it locally. Took some great photos. Got the wifi sync going with my macbook and HTC one M8, very fast transfer. Got it to connect with NFC on my phone but couldn't get the remote camera to work, won't do anything.
Not sure if to swap it or get a refund.
The A6000 is a great camera, sounds like you got a dud. I'd give it another try.
The only concerns I have are.
1. it's mostly a plastic case, how well will it resist dings and scuffs.
2. Sony very rarely updates firmware.
I've had no problems with WiFi connecting to my iPad, iPhone 4 or MacBook.
The partial PDF manual is currently here. I've yet to find a finished version of the full 200 page manual.
http://support.sony-asia.com.edgesuite.net/consumer/IM/4532055111.pdf