Yes, it indeed happens on a non-chimeric person (just try comparing the DNA from a muscle in arms versus legs, or even head hair and genital hair). I don't know the point of the study (except if it is just to undeniably confirm this scientifically because some doctors still don't believe that identical twins are not quite identical).

I would assume that the point of the study is to also quantify the amount of mutations so that future twin-based studies can more accurately attribute differences that also exist between twin pairs.

And then there is the microbiome ...

Would the microbiome be similar growing up (assuming both are living and eating the same foods in the same places/family) and then diverge later when they go their separate ways?

From what I understand, it is a continuous exchange with our environment, the same way we catch a disease.

That's interesting. I wonder what the typical variation is within a single body, versus between monozygotic twins.

Well, I can give one well-known example for this in genetics. Females carry two X-chromosome, against male's X and Y. There is one thing called X-inactivation, which means one of the X chromosome in the cell is inactivated randomly in cells. By this, even organs only carried the same kind of cells are mosaic in aspect to genes in X chromosome. Then think about a well-know X-chromosome linked disease, the Rett Syndrome, and the cell in body, in the brain.