If you’re playing the piano for an audience there are different kinds of mistakes you can make: there are those that are so trivial they go completely unnoticed; those material enough they cause the audience to pause and question; and those which are serious, obvious and your audience is certain that you’re in error.
In every case, you should continue as if nothing has happened. You are there to entertain and doing anything else would compound the mistake, diminishing your performance.
There are also a myriad of mistakes we might make when we negotiate. Errors of fact, circumstance, figures or standards, etc. They too might be trivial and unnoticed, or they might be material enough to prompt your counterpart’s concern, questioning or even certainty that something is awry.
The difference when we negotiate is that we are not trying to entertain but to collaborate. A key element of which is engendering and maintaining trust, improving (or at least not harming) the relationship.
In order to achieve this we ought to deal with the mistakes differently.
Sure, if they are trivial and remain completely unnoticed we might push on and continue as if nothing has occurred. But if they are material and they cause the other side to question, or when the other side actually believes we’re in error or trying to pull one over on them, we need to stop and address the mistake directly.
Now that might range from simply an acknowledgement and clarification, or a discussion and correction, right through to an apology and rectification.
The point is, if we are doing this as and when mistakes occur, we are actually engendering honesty and trust. We’re also alleviating a myriad of problems that can arise in the future, both with regard to the specific interaction, any future dealings and our reputation in general.