King Reza: That's not necesarily true about error. Sometimes an error is made when you are able to do something correctly, but fail to do so. An example is a ground ball hit to the second baseball who fields it cleanly and, having plenty of time to throw the ball to the first baseman, instead throws the ball way over the first baseman's head into the stands. This is an error, and the second baseman will be charged one for his mistake. The second baseman certainly has plenty of knowledge about what to do in this instance, he didn't do it.

I hadn't thought of the two words to compare them before. They usually mean the same thing and can be used interchangeably. I'm trying to think of other times when they mean differently enough from each other that only one would be proper.

He made an error. He made a mistake.
He spoke in error. He spoke mistakenly.

Least ways it's hard for me to tell them apart. Perhaps you can give an example where only one would be proper? I can't think of an example and the words seem to have the same meaning.

While building the model airplane, he made a mistake putting the propeller together.
While building the model airplane, he made an error while putting the propeller together.