The best thing that you can do when you make a mistake is to ask for forgiveness. First of all, it makes you feel better, and secondly it's the right thing to do and lastly, your list members will appreciate the acknowledgment. There is another reason, one that you've heard before:
“It's better to ask for forgiveness than to ask for permission.”
Okay, this can be a little bit controversial, but let's imagine that you have been given a really good offer for your subscribers that fits your niche perfectly, but you've already sent out your weekly message to your members already, but this has a very short time limit, waiting you subscribers will miss out. But if you send out an announcement about this special offer you've broken a promise to only send out things like this once a week.
Well, just do it, and in your sales copy apologies for doing it. This is something you should do very rarely because if you use this method too often your subscribers will stop trusting you. Save this for very, very special offers that are once in a lifetime and not to be missed. Telling your members up front what you're doing, and that you're sorry, and that they can delete right now if they do not want to read on, but that you just could not stand not sending out this once in a lifetime opportunity now is a perfectly good method to appealing to your subscribers on special occasions.
Sometimes real mistakes happen though, a list serve goes nuts, sends out emails that it was not supposed to, your site gets attacked by a virus, or worse your members are sent a virus via a hacker through your list. Sometimes you recommend a product you really believed in, only to find out it was not as good as you thought. All these things can and do happen. The best thing that you can do is own up to it, apologize, and explain how you will work to prevent such things in the future. Your members will realize that you are a human and being forgiving, as most people are, they will move on.