I would never, ever intentionally make a mistake (I agree with those who feel it's the opposite of humility), but a lot of my mistakes do get left in the finished project. I am currently working on a crib quilt that has a "moderate" mistake (it's not glaringly obvious, but it's also not tiny). When I post it here, I'll see if anyone else can spot it. :)
There are other mistakes I just sort of take as a learning experience and move on. My last quilt had some pretty amateurish-looking puffs and puckers on the top, because I hadn't stayed or starched the bias edges of my 1/4-square triangles. No way was I going to rip it out and start over, though, so I finished it the best I could and chalked it up to experience.
I have been crafting ever since I was a tiny little thing and even though I'm fairly talented, I still have plenty of "oops" moments. I'll fix the bad mistakes and the easily-fixable smaller mistakes. Everything else, I'll just suck it up and move on. :)