During my postdoc, I published two research papers as the first author, with my mentor (a Professor at an Ivy League institution) as the corresponding/senior author. Months after publishing the papers, I realized that I made a mistake in the methods section (the same mistake in both, describing an inclusionary criterion) which was unfortunately repeated a few times throughout the articles.
I brought this issue to my mentor's attention shortly after discovering it, and they said it "didn't matter" in their opinion. Several months went by, and I brought the issue up with them again because it still bothered me, and I told them I wanted to do a correction. They stated that they did not think this mistake warranted a correction and even thought I was being "moralistic" about it.
A few months later, we spoke about it (via email) a third and final time, and my mentor reiterated that they did not want to do a correction. At that point, I relented and said I would defer to their judgment on the issue.
I've since moved on from the postdoc position into a faculty job at a different institution, although I still routinely interact with my former mentor.
With all that said, I'm still bothered by this situation and feel bad about the error. I want to know if anyone else has dealt with a similar conflict. If so, how did you handle it? Is it possible to do a correction without the senior/corresponding author's blessing?