Hugh explains how to cope with a rifle that has misaligned scope-mount holes
Every now and then, a rifle escapes the factory with scope-mount holes misaligned with the longitudinal axis of the barreled action. I acquired one such gem a few years ago. I didn't have the sane man's option of returning it to the manufacturer for correction or replacement because I had immediately turned it over to an excellent gunsmith to glass-bed it, true the action, and generally set it up for high-power silhouette competition. I scoped the rifle myself, took it to the range, and discovered that with the scope's windage at its mechanical limit, I was still several inches right of center at 100 yards. Oops! That's when I developed a keen interest in windage-adjustable scope mounts.
There are three basic types. Traditional Leupold, Redfield, and similar mounts use opposed screws in the rear base to secure the rear ring. Differential tightening of the screws shifts the rear ring off center for zeroing windage without using the scope's internal adjustments. The front dovetail ring pivots in response to steering inputs from rear ring shifts.
With Weaver bases, provision for windage adjustment must be built into the rings. Weaver catalogs both steel and aluminum windage-adjustable rings for its bases, and Millett Angle-Loc rings work similarly. These rings use separate right- and left-side opposing lock screws and clamps to secure each ring, permitting you to shift front and rear rings laterally on the base.
Another, almost fiendishly ingenious, approach to ring-centric windage control is the Burris Posi-Align system. Burris Zee rings, compatible with Weaver bases, clamp immovably to the bases with a single locking bolt. All the adjustment capability is topside, within the scope ring. The steel rings are channeled to accept split-ring synthetic inserts that collar the scope tube. If you don't have a zeroing problem, use the symmetrical inserts that accompany the rings. If you need to correct a discrepancy, sets of asymmetrical inserts that exhibit varying degrees of asymmetry are available, along with detailed instructions.
If you have a grooved-receiver rimfire rifle or a centerfire with proprietary integral bases that shoots askew, you're not out of luck. Windage-adjustable rings are usually available for these models, too, although you may have to search to find them.
It's worth noting that there are mounting systems not mentioned here that also provide windage adjustability. The systems I've named are those I have personal experience with and that are available at most gun stores. Any omissions reflect the limits of my experience rather than a negative implication.