So.. I have been poking around a bit with this issue. I tried to re-do all the steps in order to see if the problem is a freak accident or reproducable. The steps done are (i know the used image is not recent!):
1) dd 2017-02-16-raspbian-jessie to Kingston SDC10G2 16GB && sync
2) Boot (RBP3B) and adjust the system (clock, locale, enable SSH and so on with raspi-config)
4) sudo apt-get update && sudo apt-get upgrade && sudo shutdown -r now
After the reboot the SD-card had file system errors. I tried twice and the errors seems to differ but both times the system was un-bootable, one time even beyond repair. Then I tried to modify step 4 to: "sudo apt-get update && sudo apt-get upgrade && sync &&
sudo shutdown -r now" and the issue was apparently not present. However, I have had issues with the Pi not always booting (red light on, no yellow activity flashing) at all with the SD-card, so the Kingston SDC10G2 may just be a bad pick for Pi.
Now I have switched to a SanDisk Ultra SD card (SDSQUNB-016G-GN3MN). I have had no issues with the above 4 steps, even if "sync" was not issued. I would, however, encourage anyone to do a sync after using apt-get, and it would be nice if apt-get itself would sync after it has done it's task. This may reduce problems with broken file systems and increase customer satisfaction with Pi
Please do not ask questions in private messages, they will not help others.