I'm mainly talking about little things; like say you're going out biking with your friend and you pump your tires and grease your chain before; you offer the pump and grease to him but he says "nah I'm fine". You take off riding, and lo 10 minutes later he's having problems with his chain and tire. The immature lesson-teacher would use this as a chance to say "I tried to tell you to prepare before the ride, see what happened!". Even if you don't do that, the immature grudge-holder would be all pissy and unhelpful about taking care of his bike. The mature response is just to forget it and be nice and say "hey I know a bike shop right over here, let's stop and get you sorted". The immature person would be all tight-faced and impatient during the stop.
Maturity comes in realizing that even though this person has fucked up and inconvenienced you, now their problem is also your problem, and you're going to still be with them for a while, so you should just get the problem taken care of and be nice so you can get on with your lives happily.
The immature side of me wants to see people pay for their mistakes. I tend to put in a lot of effort considering future risks and taking the proper protections against them. I see other people just rush into things without the proper consideration, and then they get fucked. I could them help them out, but then they are getting the advantage of not having to do the consideration work and they still get bailed out, it's not fair. It's sort of like paying for someone else's insurance. But maturity is knowing that when you do the best for yourself, you might help others much more.
A crucial factor is freeing yourself from seeing life as a competition, and not needing to prove to the world that your way is the best way. You aren't in a contest with the other person about whether taking the time to prepare was a good choice or not. He will likely make comments like "god you always take so long to get ready, greasing your chain and checking your cables, let's fucking go already". You have to just ignore that and be confident in your choice of how to live your own life.
This kind of issue obviously comes up a lot in the workplace. Maybe someone is writing some threading code, and you encourage them to clearly define the channels of communication and how they are synchronized. They're like "meh, I just write code and it seems to work, so I'm not gonna bother with that". Later they have some random hard to repro timing bug. If you're an immature cock you would remind them of their bad decision, or not be very helpful to them fixing their bug. If you're mature you just smile and help them debug their mess.
It's much easier to deal with in a strict boss-subordinate relationship (I'm the boss in this fiction obviously) where you can just tell people "do this" or "you fucked up". But even as the dictator it's wise to just relax and be positive and let people do things their own way sometimes. (and of course not everything that you think is a mistake is actually a mistake). A collegial or peer level relationship at work is much much harder to deal with. When you see a peer making what you think will be a big mistake down the road, you're in a bad spot.
One funny situation where I see this happening is in parent-child relationships. I see so many parents be total cocks to their children, using their children's mistakes as "teachable moments" (every time someone says that I vomit a little and want to punch them in the cock). They're fucking children, they don't need to be worried about preparing for future risks, that's your job, just worry for them and take care of them and don't rub it in their face or groan when they're wrong.