Formulate an answer on PhD defense about mistakes you've made
If I were on your committee, the key take-away I would look for is that the mistake will be corrected in the literature.  Either an erratum or an explicit correction in a future publication would satisfy me, though in the latter case I would ask, "What additional steps need to be completed before this future publication will be available, and how long do you anticipate that may take?"

If the future publication is still quite far away (by the standards of your field), then I would recommend an erratum in the meantime, which should do no harm.  I would not consider a long period of time since publication a very strong argument against providing an erratum.  Here is one famous paper in my field that received an erratum after 3.5 years.

A promise that no mistakes will happen in the future would strike me as naive and unrealistic.