There is nothing wrong with the G lens on the device, all the first reviews of the Z1 which stated the camera was weak or blurry in some parts were all pre-production models not running production software and most sites didn't go back to review production units with final and improved camera software.
Current sample images from z2 are also probably off pre-production devices so not final software, I've already seen 2 different camera firmware's f120 and f200 on the z2 photos and the f200 firmware clearly is a step above anything on the z1 so far, especially in noise performance.
http://www.xperiablog.net/2014/03/08/xperia-z2-low-light-sample-pictures-from-the-streets-of-tokyo/
the xperia blog shows this quite nicely, some of those shots are pretty high ISOs, the crosswalk sign is iso800 and there is minimal noise which is nuts, considering the z1 has insane noise at 200 and above. The shot of the taxis and bus is ISO1000 and it has really good noise performance vs the z1. This clearly demonstrates that the camera software in the Z2 has matured or at least moved a lot more forward compared to the updates the Z1 camera software received.
More images here, it includes the tokyo pics.
http://xdaforums.com/showthread.php?t=2673226
But again this software is not final as can be seen here, f200 software
http://www.ringhk.com/news2.php?id=8285
some of the shots are a bit more blurry vs the z1 photos which are sharper but again this can be fixed.
In your original photo you pointed out a few places on the photo that are more blurry than the rest and I agree, this is not acceptable but the original z1 reviews stated a right sided blur which people said was due to a flaw in the lens. But this flaw is not apparent on all photos meaning it probably was a software issue rather than hardware.
Therefore the same issue is most likely present here as mentioned by others, software still not 100% final. Bionz for the z1 when released was no where near what it should have been, in fact it still isn't anywhere as good as what sony states. The Z2 is Bionz mark 2, and has much more improved performance and will no doubt be a much better product once the production units are released.
As for the Barcelona shots you posted, they are unfortunate and not acceptably but then browsing them I noticed one thing, they are in a helicopter and the user is shooting the photos not using only the Sony but also though the windows of the helicopter which adds another factor in front of the lens which can distort the image.
I'd wait for production models and production sample images and not basing off pre-production models.
