Current practice in many Ashkenazi synagogues includes the following:
On shabbat zachor, repetition of (at least part of) Devarim 25:19, due to a doubt over whether the zayin of זכר is vowelized with a tzere ('five dots') or segol ('six dots').
On purim, repetition of (at least parts of) Esther 8:11 and Esther 9:2, due to a doubt over whether the correct text is להרג or ולהרג, and בפניהם or לפניהם.
As far as I understand, today we can be very confident that the correct versions are (respectively) זכר with five dots, ולהרג and לפניהם.
However, I have noticed that for parashat zachor the 'correct' version is read the first time, but in megillat esther the 'correct' version is read the second time.
Why is this the case? Is it simply that the 'original' Ashkenazi practice happened to be the 'correct' version for parashat zachor and the 'incorrect' version for megillat esther, and then later customs developed to append the alternative version?
Do any sources (which advocate for or at least don't dismiss out of hand the custom of repeating verses) discuss the recommended order of the repetition, or describe an order different to that which I have observed?