"To err is human, to forgive is devine" There isn't one of us walking around sucking up air who hasn't made a mistake. As for those of us willing to admit it, well that's another story :).
Personally, I'd rather someone make a mistake of effort as opposed to one of neglect or laziness. Most of us would find that kind of transgression far more forgivable. Also, when you do goof, the most mature thing to do is own up to it, as opposed to covering it up, or outright denying it. This does two things: it makes it possible to make amends or corrective action to address it and also enables the situation to transition to resolution and, hopefully, on to forgiveness. It also takes away the power of blame. It always amazes me when I come forward and admit my error, and offer a sincere apology, that it takes away all of the righteous anger of the person wronged and softens them. I've even seen the other person go from an 8 or 9 on the irritability/anger scale to almost copping some of the blame themselves for my mistake and having it bond us closer than before!
Conversely, when someone makes a mistake that directly impacts you, however much you are in the right and difficult it might be, do try to treat them as fairly as possible and forgive them. If they refuse to admit, take their blame or acknowledge their role, still try your best to let it go. This is more for your benefit than theirs ultimately. Certainly don't give them a chance to wrong you again, there's no dignity in being a floor mat or a sucker. Realize that harboring ill-will and anger is never beneficial on your end. The toxicity of that rubs off on you whether you're in the right or not. Have faith that those who refuse to apologize or acknowledge their role in doing wrong, will reap what they sow and let nature run it's course.