Hi Ken,
I am nearsighted enough, and I hope, optically inclined enough to take a stab at your questions. I have also used an individual-focus binocular, which has each eyepiece focus setting marked in diopter units, which has increased my awareness of these issues. Not quite an MD in opthamology, but those are my credentials and here goes.
Does it compensate for differences in distance vision?
Yes. It compensates if the two eyes are not equally farsighted or nearsighted.
If both eyes are corrected to 20/20, should the wheel be at the center mark (assuming it was put on correctly by the manufacturer)?
Yes, if both eyes are 20/20, or also if both eyes are equally nearsighted, or equally farsighted, it should be at the center mark.
Or, if one eye has a problem that makes vision in that eye less clear than the other, does the diopter adjustment affect that?
If the problem is a difference in farsightedness or nearsightedness, for example one eye perfect and the other simply nearsighted, it will. But if the difference is some more pathological problem or to the extent that either or both eyes are astigmatic (focusing error due to a more arbitrary misshaping of the eye's optics, ie, the eye's lens is lumpy), it won't.
Finally, if the diopter number is + (where the diopter wheel is on the right barrel), does that mean that the right eye is weaker or stronger than the left?
I don't know which you mean by strong, farsighted or nearsighted. But, a right-barrel + adjustment means the right eye is more farsighted than the left, analogous to a presciption for eyeglasses. Just like if you were farsighted, your glasses prescription would require convex, converging lenses, which are said to have "+" power. If your right eye was more strongly farsighted by one diopter, then, if the right-barrel adjustment was marked in actual diopter units, it should be set at +1.
The diopter is the unit if lens strength. It is the inverse of the lens's focal length in meters, and taken to be positive if the lens is converging. This inversion is done so that more strongly focusing lenses will have higher diopter values. This makes better commons sense to most folks, but also carries a handy mathematical simplification: "diopters add". For example, two converging lenses, strengths 2D and 3D, placed close together will converge the same as a single 5D lens.
End of my knowledge, so end of lesson! Hope that helps.
Ron