I have a Nikon 2X EER scope on a rifle, in Scout confguration.
With the rifle held steady, I notice that the reticle point of aim changes if I move my head.
Is this typical of EER scopes, or is there a scope problem.
If typical, is it common to all the EER scopes including Leupold?

This is called parallax, and it will show up to a lesser or greater degree at any distance, longer or shorter, than that at which the scope's parallax is corrected for. Scopes are generally corrected for parallax (no apparent target movement) at a pre-determined distance. For non-adjustable rifle scopes, this is usually about 150 yards. For rimfire, pistol, and shotgun scopes, this is usually about 60 or 75 yards. A scope with an adjustable objective or side-adjustment parallax knob can be adjusted for any distance from its minimum (usually about 50 yards) to infinity.

If you are sighting on a target which is a great deal closer than 50 yards, you will see parallax. This is true with any scope. There are some optical tradeoffs that can reduce parallax, and some of those are typically incorporated into Leupolds, so you might find less parallax using a Leupold than with the scope you currently have.

I do most my load developement at 200 yds. In the last year I've seen 3" movement at that distance from Leupold, burris and bushnell elite scopes.
Some were mine and some were friends. All were sent in and all tech depts agreed it was too much. All came back with virtually no movement at 200 yds. Not sure what the bottom line comparison would be with what I now have at say 500 yds but I think I like my results.
It kind of boggles my mind that all these companies offer long range ballistic and mildot reticles....then set parralax at such a short distance that you can see the cross hairs move all over the target at just 200 yds.
BTW....one positive is on the burris scopes it was an opportunity to have them install a hunter elevation turret for just $40....it's really nice and I think a quite a bargain for what they charge.

No scope is or can be paralax corrected at anything but a single distance, it's a mechanical thing based on the lenses involved. (How well the human eye can resolve any slight lack of focus, and paralax, is a different question.)

Paralax is when the point of focus in which the image being viewed lies at a different place than the reticle. If it's focused closer than the reticle the viewed object is farther away, vice versa. It's not necessary to understand all this but most photographers call it "depth of focus", and it's not quite the same thing as depth of field.

Paralax is more conspicus on higher powered optics, less so on low powers. You have to move your sighting eye quite a bit to see it in a 2x optic. Paralax and where the focus plane falls inside the tube is irrelivant IF the user keeps his eye in the center of the scopes exit pupil.

Seems few people focus their optics properly. The front (objective) lens is known so the scope can be mechanically adjusted in focus at the cross wire for what ever range the maker feels is proper for that scope.

The rear lens (ocular) must be user focused on the same cross wire or everything will be off. All we need do is look through the scope at a clear sky or white wall and adjust for the best focus on the cross wire and we are done.

If we cannot get everything in sharp focus that way it's time to send the scope to its maker for correction.

I believe the Nikons (and Bushnell 3200/4200s) I've seen are fully equal to my Leupolds.