A billing error occurred due to a host migration oversight, resulting in some customers receiving two email receipts as they were accidentally charged twice. This mistake happened because nightly billing jobs were unintentionally left running on both Engine Yard and Rackspace, leading to duplicate charges. However, the issue was swiftly resolved by utilizing Braintree's API to void the second charge with minimal coding effort. The author, PJ Hyett, acknowledges the error as avoidable, expresses embarrassment, and assures customers that the situation has been rectified, inviting them to continue enjoying GitHub's services.