It kind of depends upon what the “mistakes” were. Cheating, IMO is not a mistake, it’s a conscious decision to do something wrong (assuming that you are not in an open marriage).
But let’s say it was cheating and that you want to keep the relationship together. I think it’s crucial to get couples counseling to sort it all out and get to the root of the problem and for the cheating partner to be made clearly aware that what he/she has done to the cheeted upon partner has created pain and uncertainty and loss of trust.
Then, I think it is crucial for the cheating partner to become more accountable than he/she was before. The cheater needs to make sure that the cheated upon partner is made to feel comfortable. They need to make sure they tell the cheated upon partner where they are going to be, to call if they are going to be late or go someplace else, and make sure that the cheated upon partner is OK with that. It’s not fun for the cheater, but I think it’s necessary, otherwise it will be business as usual, and the cheating is much more likely to happen again.
The cheater must also realize that the pain and uncertainty will never completely go away, and so they cheater must actively decide that he/she won’t tell the cheated upon partner to “get over it” or become resentful, they need to go above and beyond the call of duty to fix the relationship or call it quits.
But the cheated upon person must also do their part to not bring up the subject constantly.
And the cheated upon person must be given a lot of leeway regarding “checking up” on the person. The cheater should allow open access to e-mail, FB and phone messages. It sounds harsh, and maybe unfair, but unless a couple is open and honest, there is a pretty good chance that the cheating will happen again.
If you are talking about other kinds of mistakes, please give us some examples, the advice might be different.