Possible BIG problem 16-50 with Nex 6!

That would happen when the autofocus chooses a wrong focus plane for some unknown reason. Like a dust spot or it is fooled by some internal reflection or by some coating layer on the glass.

I assume from your pictures that this happens also with good lightning conditions? Like with iso 100/200, 1/200th second pictures? I see with my nex (although it's an old one) that the AF performance drops signifficantly in poor light.