The first thing I noticed about my NEX-6 was the fast speed of response of the shutter, the delay is very short indeed, After dong a bit of research I found that the shutter is 'opened' electronically and closed mechanically. The 'Front curtain shutter' entry in the settings menu controls this behaviour.
When using Sony lenses in manual focus (or DMF mode) the camera can be set to zoom in when the focus ring is turned. This works because the E-mount lenses use fly-by-wire focus so the camera knows that the focus ring has been turned.
One of the features of mirror-less cameras is the small distance between the lens mount flange and the sensor. That small flange to sensor distance opens up the possibility to use adaptors to mount older manual lens on the camera. If you can afford them, you can mount Leica M-mount lenses on a NEX, these lenses have the advantage of being designed for a mirror-less film camera which itself had a short mount to film distance. I don't have that kind of money to spend at the moment!
When I first received my NEX-6 I thought that one of the things I was going to have to live without was depth of field preview. On a DSLR DOF preview is accessed by a button which causes the lens to stop down. After experimenting with manual focus I realised that on the NEX the lens is normally stopped down which means that the camera is normally showing DOF preview. Even better, because of the electronic view finder the image is always bright.