To leverage Twilio's Debugger Alert Triggers, developers can create a Python application using Flask that listens for requests from the Twilio Debugger, processes and stores relevant error events in a CSV file on their local system. The application can be secured by validating the origin of incoming requests using the Twilio Helper Library and rejecting any invalid requests. By filtering events to only consider those coming from specific webhooks or with specific error codes, developers can collect valuable data about errors occurring in their Twilio applications, such as the URL that encountered an error and the error code. This application provides a useful tool for debugging and maintaining production webhooks and applications built on Twilio's products.