Mistakes are vital experiences not only in novel writing but in real life as well.
They are just as embarrassing and driving for a character as they are for someone in reality. The way a character reacts to one of their own mistakes is a huge reveal about the type of person they are.
And in all honesty, the way a real life acquaintance reacts to a mistake is very telling to me to. Just like characters in stories, we find out very quickly how far we can trust another individual with how they choose to deal with a mistake.
Does this person try to blame it on someone else?
Does this character try to hide it under the table?
Do they immediately take responsibility and correct the error?
The above are just a few telling examples of character and to go even further, culture.
The longer you live and travel, the more you realize that different cultures have different ways of dealing with errors, and the severity of the punishment or mercy depends on the characters of rulers and of the people.
Everything about mistakes from the micro level (individual) to the macro (nations and world) creates a driving factor for stories and should be embraced by the writer as a not only a reflection of reality but also as a tool for an intriguing plot.
Because really, who wants to read about a character who never has any obstacles to overcome or never has to apologize? It is one of the spices of writing and an everyday experience we are all too familiar with.
I learned a long time ago, and I am still learning, that to embrace my mistakes and work through them makes for a better story in the long run and creates better character development in the progression of my own life.