A proper apology is not just “sorry,” but includes an acknowledgment of what they did wrong and that they’ll avoid doing the same thing again. Showing that they realize the nature of the problem and will at least pretend to not do it again would be good.

Yes.

"That was a mistake, won't happen again" is an acknowledgement that they got it wrong and a promise not to do it again.

"We're changing it" is neither one.

It'd be the same kind of "We're sorry" as the South Park BP oil spill commercial.