I have miss-drilled the hole for my doorknob. Is there anything I can do to cover this mistake?

One option is to use a brass door reinforcer. This product will also increase the strength of your door.

Check your state and local codes before starting any project. Follow all safety precautions. Information in this document has been furnished by the North American Retail Hardware Association (NRHA) and associated contributors. Every effort has been made to ensure accuracy and safety. Neither NRHA, any contributor nor the retailer can be held responsible for damages or injuries resulting from the use of the information in this document.