I've been in various analagous situations, and the following is a dream-list for how I wish things had worked.
In an ideal world, one should be able to make non-essential arxiv updates (typos etc.) on published papers without it generating a new version. This would encourage people to correct minor errors, which can actually seriously confuse a reader. I know that I would not put a new version of a paper on arxiv after catching typo-level errors, although I also know that this is bad for readers.
For more major errors, I wish people would keep errata for their papers on their webpage. For fatal errors, published errata may be necessary.
Politics gets in the way of this working properly, because the incentive to "be friends" is stronger than the inventive to plug minor holes in correct results. This would not be the case if we were doctors working towards a medicine to save the lives of sick loved-ones, for example... then we would care about catching the minor errors too. And so, I wish people aimed for perfect papers more seriously.