Shipping clean code at Sentry involves using a combination of linters, auto-formatters, automated testing, visual diffs, measuring test coverage, and detecting package vulnerabilities to ensure the quality of the code before it is deployed to production. The use of continuous integration and deployment (CI/CD) tools like Travis CI helps to reduce bugs and improve observability. Sentry uses a range of tools including Percy for visual diffs, Codecov for measuring test coverage, and Snyk for detecting package vulnerabilities, to achieve this goal.