There's something you need to learn about people, Flyme...
Most dislike taking responsibility for mistakes.
I always take responsibility for mistakes that are mine. It's a good habit, especially at work, because if you try to bury your mistakes they eventually come out anyway and it either looks like you were hiding it or you're clueless. Better to just rip off that bandage and own it.
That said, if I can catch the mistake and jump in with a fix before anyone notices, that's the best-case scenario.
Plus, everyone gets used to you taking ownership of the things you did wrong - which means they don't have to wonder about what else you might have done wrong. Take a guy who never seems to make a mistake: what horrible screw-ups has HE done that he's desperately trying to avoid? Everyone makes mistakes.
And occasionally when someone is a tiny bit at fault and I pick up the tab because it's mostly my fault, their relief at avoiding the minor social stigma of having made a mistake reinforces my value to them.
One possible downside is that because I agree that I made a mistake when I did it rather than sweeping it under or ignoring it, it may seem like I make more mistakes. Also it's possible others may begin to view me as a possible scapegoat for their own mistakes.
I think these can be mitigated by cultivating an atmosphere that internal mistakes are expected and what matters is that they're caught before being sent out into the world. And most importantly, by maintaining honesty and integrity I can better defend against social attacks such as baseless blame from a self-serving coworker trying to shrug responsibility for his own mistake.
Anyway, that's what I'm doing and we'll see how it goes. So far so good, after 6 years in the workforce, honesty tempered by social agility has served me well. I'm still a beginner though!
I suspect that people who are very good at deception and manipulation can get ahead faster but with a risk of catastrophic failure. But I suspect ambition is more important than the method used to fulfill that ambition; while the method has an impact, the will to power is the deciding factor.