From the mall last night. I know the 16-50 gets no love from the testers but it is better than they would have you believe. I went to the mall last night and did some candids. Most people thought I was looking at a cell phone and paid no attention to me. This shot was at 16mm f/11 ISO 3200 and 1/20 of a sec
Wow, 3200ISO and the picture is clean, clean, clean.......I love Sony sensors

I dont think the lens is to blame here, just not very good composition, malls with their lighting and our general tendency to feel uncomfortable feeling of shooting in such busy places is not the "best" place to really get the best out of us and our equipment.
I am sure you will get much better shots in a different place and different environment.
The a6000 looks very impressive to me.
The sensor and in-camera processing are really great. The live view from the tilting monitor compared to my D7000 is outstanding. (I've heard that the d7100 is a little better) The eyelevel finder is a mixed bag. In low light it brightens which is nice but, the refresh rate is too slow for fast panning. The 16-50 is so so and they are offering a 16-70 f/4 Zeiss that has tested much better but, it comes at the price of $999!!!
You see for me there are 2 kind of zoom lenses, F2.8 and everything else.
F4 is just Waaaayyyyy to slow for me.
With F2.8 I get a very big lighting range to work with while F4 is not flexible at all and I am talking from a FF POV, crop sensor is even more limiting.
I say it again and again, Sony makes good product but for some weird reason is concisely limiting their cameras with slow lenses, don't know why but they do.
Mirrorless is still a little behind DSLR in some aspects, I am sure it will not take long for these engineers to figure out how to improve it.
For now the a6000 is probably one of the best mirrorless you can buy.