I'll try to explain this...
"I don't hesitate to make a mistake" means you are eager to make mistakes on purpose.
"I don't worry about MAKING a mistake." You worry about things, not actions. "To make..." is an action. "Making a mistake" functions as a thing. The meaning of the sentence is that you think you will never make a mistake.
If mistakes don't worry you, then Eliot has given you the proper suggestions.