Ethics for Aristotle is primarily concerned with ethos (dispositions to act in particular ways, associated with character and culture), and only secondarily with particular actions. Particular actions are mainly addressed in a higher-order way, through discussions of practical judgment and responsibility. We should try raise people to have good character, and we should generally trust people with good character to do the right thing.
For Aristotle, perfection is always perfection according to a kind, and perfection according to a kind is understood in such a way as to be actually achievable. The Greeks in general had a concept of blamelessness that was considered to be achievable. The world could do with a lot less blame; we should learn from this.
I would say you are blameless if you have done all that is within your power (and you are a hero if you in a meaningful way actually take responsibility for things that are beyond your power). If you really act from a disposition to recognize others as independent of yourself and your wishes — as one would a friend — and are reasonably attentive to circumstances, then you cannot reasonably be faulted for your actions, and your conduct will be blameless. If one has been well socialized, being blameless is not really all that hard.
A blameless person can be wrong, and can even do things for which apology is appropriate (because of an actual bad effect, not any blameworthiness). But if you consistently recognize others as independent of your wishes and take reasonable care that your words and deeds are appropriate to the situation, then you are blameless.
I think the practical import of this stands even on the basis of Brandom’s innovations (see Rethinking Responsibility; Expansive Agency; Brandomian Forgiveness). Adding back in a responsibility for unintended consequences that is shared with many others and whose failures are forgiven should not negate what I am calling blamelessness.
I also think that blaming in general serves no constructive practical purpose. To blame someone is basically to say they deserve punishment. Punishments resemble vengeance; they may be deemed justified in some circumstances, but we should not fool ourselves that they are constructive. Punishment per se does not improve anyone’s ethos. Either someone really gets the message that they did something wrong — in which case there is no need for punishment — or they don’t, in which case it is unlikely that punishment will change that. I don’t pretend to have a general solution for crime in society or for misbehavior of children, but I distrust the impulse to punish. Fear of punishment sometimes prevents bad behavior, and sometimes behavior is what counts, but fear has nothing to do with moral improvement.