Jason Etcovitch shares insights into enhancing productivity and efficiency through innovative uses of GitHub's API, Actions, and Probot. GitHub Actions serve as a versatile tool for automating tasks within repositories, allowing users to run custom code in response to events, while Probot provides a framework for building GitHub Apps that react to webhook events. He highlights features such as creating dynamic content with pinned Gists, automating branch deletions post-merge, and using GraphQL for retrieving detailed resource information. Additionally, Etcovitch emphasizes the utility of URL extensions for accessing avatars and commit diffs, encouraging developers to explore and share their own tips through the #GitHubProtips initiative.