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Sean,

Just a little more... 

Since the resolution of good, corrected vision is about one minute of arc you should expect 1-2 minutes accuracy in sights when you're using a unit magnification sight tube, and that's what I usually find. Notice that key adjective "corrected". Do you wear glasses or contacts? In addition to magnification, a telescope provides optical focusing and allows fine correction of vision. With a sight tube, you don't have that luxury, and you need to make sure you're using any long-distance optical correction you need (eyeglasses).

Another concern with a unit magnification sight tube is collimation of the line of sight. Collimation error arises when the line of sight isn't exactly parallel to the frame of the instrument. When looking through a sight tube especially, you need to make your "contact" close to the vertical line of the field of view. You can detect this by bringing the Sun into contact with the horizon, and then "panning" left and right. This is a lot like swinging the arc but for a different reason.

While I'm thinking of it, notice that it's not really "zero" magnification, but "unit" or 1x magnification if you want to be consistent with the usual method of describing magnification. That's a trivial matter, of course, and clearly we all know what you meant by "zero" magnification.

Frank Reed