King Reza: You did find some examples! :)

This isn't my bill. There must be an error.
I made an error about Julie. She's nice, really.
It was a huge error to send her to boarding school.
A week after the wedding she realized she had made a terrible error.

>Make no mistakes, we're facing a major financial crisis.<this is a different use of mistake. Kind of idiomatic and it won't look or sound right putting error in its place.>The accident was the result of pilot mistake.<
This might be a legitimate sentence, but as you have it is the way I always heard it.

Rising costs have left us very little margin for mistakes.