Part of me wants to say that the accuracy in a micrometer is primarily in the male thread, not the female threads it fits in. Inaccuracy seems to depend on that male thread and it's consistency along all of it's length. The length of the male thread should be the range of the micrometer (usually 1" or 25 mm) PLUS the length of the female thread. So, as long as the fit of the male thread is consistent along all of it's length, it should work equally well at all points in the female thread.
But another part of me says that we are talking tenths and even hundredths of a thousandth of an inch and things can go wrong in unexpected ways.
On the use of a tap, I would be more worried about the class of fit after using one instead of a loss in the pitch's accuracy. Taps come in different classes of fit and you positively do not want to open up the female thread so much that it would result in a poor fit with the male thread. But since there is an existing thread which is probably good except at those few spots, using the tap probably would not result in any interference due to any small differences in pitch. What it could/would do is make the existing, female thread somewhat looser, at different places along it's length. So only those places that are less changed would provide the working part of that fit with the male thread AFTER adjustment for the fresh cut. And those remaining areas that do all the actual work will wear faster than others in the female thread so it will need adjustment more often as it wears in.
I do wonder how the damage you describe could have been produced. Just knocking it around or dropping it would have applied equal amounts of pressure all along the thread, not in just a few, small places. Perhaps some kind of contamination got in there and lodged in those spots? You may want to look at the male thread under magnification.
It is a Starrett so it should be of pretty good quality and therefore worth saving. I would call Starrett and ask if they can repair it. Using Starrett is a definite suggestion if it is a model that reads to tenths. If it only reads to thousandths, you may want to risk the tap. But in any case, I would talk to Starrett FIRST.