I suspect I could answer this question myself, except for a couple of things: my geometry-fu is weak, plus I don’t know how or what to measure in order to exercise what feeble geometry skills I do possess.
Over the years, at a rough guess, I’ve bought and installed maybe ten different scope mounts and bases, and helped friends with maybe that many more. At first, I just bought Weaver rings, the really simple ones. This was before you could get anything you want on the internet.
Then, as I began to encounter different combinations, and occasionally a scope that “ran out of adjustment”, I started buying adjustable bases.
I’m not a person who is inclined to thoroughly test out a rifle at all ranges when sighting it in. My usual procedure is to sight it in at 25 yds., then test it at 100. I look at ballistic tables and guesstimate other ranges, and since I probably shoot at ranges greater than that maybe once a year, this lazy approach actually fulfills most of my needs. I AM more careful if the rifle/scope is meant for longer ranges.
So this question is theoretical to some degree.
As I said, most of my recent bases have been of the windage-adjustable type. And they have, as far as I can remember, always solved the run-out-of-adjustment problem for me. (that, or re-assembling the base and mount; making sure it’s on right)
Then, usually, on the way home, I think, “what have I done?”
To my way of thinking, the line of sight thru the scope MUST be absolutely parallel to the bore of the gun – I can see how one might want a slight forward cant for elevation, but otherwise, wouldn’t windage adjustments to the base tend to skew your adjustments at different ranges and so on?

So my question has a several parts:
How do I assure myself that my line of sight is parallel to the bore?
How much difference would a few screw turns make anyway? ( It would seem a lot – they are for GROSS adjustment!)
Finally, how would someone know if the manufacturer didn’t machine the screw holes parallel to the bore in the first place? Would a deviation of a few thousandths of an inch cause a perceptible shift downrange at longer ranges?

On question 3, i would say the holes will likely be off, if they were perfect it was probably accidental. Even if they were y our scope and mounts would probably off a little too.

On question 4, I would guess a little.

I have a lot of questions like these too, they're not really precision shooting questions, but i kinda quit asking, until i can buy some property and build a long range shootiing range.

i kinda quit asking, until ....

I know THAT feeling...

The shame of it is, I have the property; I even have a sort-of-"range", and the time I have available to test each load at 25, 50, 100, 200, 300, and so on has its practical limits.
I should say while I do have a few shots on my property that are beyond that, I'm not really all that interested in shooting beyond, say 400 yds, as a routine thing. Not enough to develop special loads and do the practicing.

If I knew what error, for example, a mounting hole being .001 further from the bore than its partner, I might figure out that it only would be a concern at ranges beyond that. The same applies to gross adjustments in the base.

I guess I could amend my question to...
Has anyone experienced any weird sighting-in behavior that could be attributed to misalignment of the scope (or other sight) and bore?

Thanks 4 the reply, Ratgravy... ya'll got rained out in Louisiana yet?

Yep, everythings soggy now. It stopped though.

I've never tried it but i wonder if mounting an upper in a vice and stretching some thread or even shinning a laser through the bore then another piece stretched parallel just above would reveal misalignment of mounting holes or mounts.

Okay, let me start of with a somewhat smartass response.  We're friends, so I think I can get away with it

How do I assure myself that my line of sight is parallel to the bore?

Well, if your scope and bore are completely parellel, the bullet will never cross the line of sight.  It will start out low, and keep getting lower -- unless you're shooting upside-down, in which case you have other issues to deal with.


Now for my real answer, preceded by a disclaimer.  I don't have much experience using scopes on ARs.  Most of my serious scope experience has been on bolt guns, so most of the following are assumptions based on applying that knowledge to what I know about ARs.

The most accurate results will come mounting a good quality optic as solidly as possible to the upper.  The more intersections of rings, mounts, adjustment points, etc. you add, the more potential weak points you are introducing.  So the most solid platform should be a set of rings that attached directly to the upper, and is machined to tight enough tolerances to stay reasonably concenctric to the intended bore line.

The next most important thing is making sure your scope is mounted solid and LEVEL in the rings.  If the scope is canted, you may be dead on at your zero range (whether it is 25 or 200Y), but if you adust for drop and try to shoot inside or outside that range, you will be off.

The main reason I know of for doing initial zero of your scope with an adjustable base is to ensure maximum adjustment range for windage and elevation for extreme long-range shooting.  I don't think this is on  your agenda, so is probably not as big a concern for you.

Those are my semi-educated thoughts on the matter.  I'm sure someone else will chime in with more solid experience, and probably tell me I'm completely wrong.

Ratgravy... I've actually tried that, well not exactly the bit with the laser, but boresighting; plus I have one of those Leupold boresighters. Another technique is to find a dowel rod of about 30 mm, put it in the rings and visually align it.
The trouble is, I'm not convinced that visual observation is enough...
I'll try phrasing it this way: A minute of angle is, I assume, 1/60th of a degree. At 100 yards, it subtends approximately 1". It's observable at 100 yards... you can't see it at boresighting distances.
The other day, while mounting a Leupold to my new Varminter, I used the boresighter, which showed that the scope, as mounted would impact a few MOA to the left. I adjusted with the windage screws on the base - it took just a few turns of the screw.
Now, was it parralel to the bore to start with, and is it now twisted so that it will be accurate at one particular point, and off in both directions at any other point, or vice versa?

Oh, well. I'm about convinced that Ratgravy's point is valid - there ain't no substitute for taking it out to the range.
Isn't that what you call "empirical evidence"?
( "empirical evidence", existentialism, parallax, and now precise alignment of scopes... just another one of those things God didn't mean for me to comprehend!)

Since where the crosshairs intersect in a scope (any scope including red dots) are a single reference point relative to where one is expecting the projectile to impact, any "non parallel" issue is accommodated by adjusting them to the point of impact.  Almost every scope mounted does not mount perfectly parallel to the bore which is why the firearm  should be bore sighted and shot at known distances to achieve "zero". Gross alignment issues are made by either adjusting the windage screws (as with a Redfield or Leupold sets of rifle base/rings) or shimming the respective base for elevation or nonadjustable rings, if possible. If one looks back at the early fixed (non-internally adjustable) scopes, all adjustments were made by external means.  In these days of internally adjusted scopes, all but the most egregious problems can be made by using the elevation/windage screws on the scope.  Most common serious problems encountered are windage issues and that is why companies like Redfield, Leupold and other similar patterned rings/bases, offer windage adjustments on the back ring.

The most common problem with mounting scopes is not the "parallel to the bore" issue as much as having the cross hairs parallel to the axis of the rifle, i.e. canted.  If there is any canting, it means that if you move the crosshairs up, then the point of impact will also move left or right at the same time by some degree. Eliminating or at least minimizing canting will ensure that as you make any adjustment to your scope will not result in changes to point of impact on the other axis.  

If one is a long distance shooter, you wouldn't want to move your elevation up to accomodate a longer shot and find you also moved the POI left or right by an 1" or more, would you?

Most common serious problems encountered are windage issues and that is why companies like Redfield, Leupold and other similar patterned rings/bases, offer windage adjustments on the back ring.

<Bob excuses himself to go check rifle with said bases, and make sure that adjustment screw was in the rear. It was.>

Seriously, though, you make a valid point re: canting.
Like I said in the beginning, my geometry-fu is weak; but even discounting the built in errors, it's just kind of off-putting to not have your cross hairs running straight up and down.

I wonder what happens if you have a single dot as in some reflex optics? My point is, I hope there is some way of mechanically lining it up - "...having the crosshairs parallel to the axis of the rifle." Otherwise, you could make yourself really crazy trying to sight it in.

Quoted: Most common serious problems encountered are windage issues and that is why companies like Redfield, Leupold and other similar patterned rings/bases, offer windage adjustments on the back ring. <Bob excuses himself to go check rifle with said bases, and make sure that adjustment screw was in the rear. It was.> Seriously, though, you make a valid point re: canting. Like I said in the beginning, my geometry-fu is weak; but even discounting the built in errors, it's just kind of off-putting to not have your cross hairs running straight up and down. I wonder what happens if you have a single dot as in some reflex optics? My point is, I hope there is some way of mechanically lining it up - "...having the crosshairs parallel to the axis of the rifle." Otherwise, you could make yourself really crazy trying to sight it in.

About the only way to solve canting in any scope, including red dots, is to use any available machined flat spot on the firearm, set it level , lock it in a cradle or vise, and then use a level on any flat spot on the scope or a known level square to align the crosshairs (flats only an a red dot). You just have to hope that your scope wasn't made by a crosseyed machinist and/or on a Monday!

BTW: Some left handed folks (and others) like to rotate the scope 90 degrees counter-clock wise to move the windage knob out of the ejection path.  They then have to remember elevation is now windage and windage is elevation.  My Aimpoint has the knobs marked for either position.

I agree with everybody here. Getting a scope to align correctly is a pain in the ass. The worst part is that since all errors are accumulative no matter how small the error is, it just all adds up.

I usually use a machinists rule to check for the straightness of the tapped screws on top of the receiver. Unfortunately, that doesn't tell you if the screw holes are straight down the axis of the bore. But, a windage adjustable base can reduce that problem.

And if the tapped holes are off center in relation to each other, you may still be able to use a one piece base. If there off more than a bit, you might be better off using a two piece base. Either way, the scope may end up being slightly twisted in the rings. So you may consider lapping the rings at this point.

Then there's the whole bore sighting thing. I still use the kind with a spud in the end of the barrel and a grid in the sighter. The problem with these are how well is the spud sitting in the bore. Too tight a fit and you take a chance of scratch the bore or causing damage to the crown. Too loose a fit, and the sighter keeps falling off to one side or the other. Then there's the problem with the grid itself. Is the Zero/Zero point actually in the center of the sighter, or is it off to the side. One day, I'm going to get one of those lasers to see if they work any better. One day.......

To change point of aim to match the point of impact, the  entire reticle (a single unit whether it's wire filament or glass) is actually tilted in one direction or the other in relation to you. The job of the reticle is to help you fool yourself into thinking that the reticle is at the same vertical plane as the target. So, you tilt it one way or the other using the adjusting screws which angles the reticle and bends the path of the light being retransmitted down the tube body moving point of impact and changing line of sight.

Also the most important part of the reticle is the aim point. That's the intersection of the cross hairs on the dot in a red dot. So, if your cross hairs aren't absolutely verticle, that doesn't effect your aim point on the reticle. What it does do is give you something else to think about while you're supposed to concentrate on the aim point, and you're off the mark for the shot.