We all make mistakes, it's a fact of life. What is more important is how we react to and deal with them after the event. This includes other people's mistakes as well as our own.
Let's start with other people's mistakes. Do we gloat over them, revel in their discomfort, or actually try to help them? Our actions regarding other people's behaviour mark us as much as our own actions do. Yes, there is always going to be the person or occasion where we think "it was coming to them" or something along similar lines, but most of the time we will feel guilty afterwards, or realise we've been a bit judgemental. After all, we could have so easily be in the same situation and done the same thing wrong. At the end of the day we're all human and none of us are perfect. The problem here is if we always have the reaction of being pleased when someone else has failed or made a mistake. Do we really want to be this kind of person? Or if someone else is like this, do we really want to be associated with them? How do they react to our mistakes? It's something to think about and ponder on.
Onto our own mistakes. Not only do we have to deal with other people's reactions (upset, pain, gloating, laughter, etc.) but we also have to deal with our own reaction to them. As with everything in life, there are extremes (usually unhealthy) and a more balanced (healthier) middle ground. You may be the sort of person who just doesn't care, or al least appears not to, and just puts mistakes down to experience. They are in the past, done and dusted and not to be dwelled on any more, disregarded even as not really having been a problem or mistake in the first place, more along the lines of other people making a mountain out of a molehill. The other extreme is to be dissecting everything and studying it minute detail, to the extent that it gets blown out of all proportion and becomes a seemingly much bigger problem or mistake than it actually was in the first place, making yourself upset and more in pain in the process. Ideally, we want to walk the path somewhere in the middle here. We shouldn't disregard what we've done, especially if it's hurt or affected other people, we need to take responsibility for our actions, but at the same time it's not going to do any good dwelling on it indefinitely or becoming a martyr over it.
At the end of the day, we need to acknowledge that no-one is perfect, we all make mistakes, but we need to try and learn from them to stop us repeating the same ones over and over again. We need to try to help others rather than laughing at them when they make mistakes too. We need to try not to repeat past habits that are harmful to us, to stop hurting ourselves over our mistakes and regrets, and to move on from them without punishing ourselves any more.