To debug and monitor Netlify function errors effectively, developers can leverage Sentry, a powerful error tracking tool with built-in integrations for nearly everything, including HTTP Toolkit. Setting up Sentry requires creating an account, project, and DSN variable in the Netlify build, then initializing the Sentry SDK. To catch handler errors, developers create a reportError method to wrap function handlers, catching errors and reporting them to Sentry. For reliability, they also need to wait for reported errors to be fully sent and prevent Sentry callbacks from interfering with normal Lambda shutdown. Optional extensions include extra reporting and including the function's git commit as the Sentry release. With these steps, developers can set up reliable error reporting for their Netlify functions.