In orthographic view I always see the vertices that should be hidden (i.e. behind the view, x-ray) as well, even though x-ray is toggled off.
I have followed a youtube tutorial and changed all relevant settings to milimeter, could this cause the problem?
EDIT: The suggestion below that it could be z-fighting turned out to be right. I had to lower the "end value" in the viewport view settings from 5 million to 5000 for the problem to go away.