The amount of footnoting and documentation depends on the nature of the mistake and the length it has been in publication.

A grammatical correction from 10 minutes ago would be on the far end of the “don’t bother to note it” scale, while something like a revised opinion based on new information would be worth making a public note about.

As Guanxi88 noted it will show a pattern of growth. It will also take the propaganda value out of “outing” your changes.