In a blog post by Gleb Bahmutov, the challenges of assertion counting in automated testing using Cypress are explored, specifically focusing on scenarios where tests finish prematurely before all assertions are executed. The post illustrates this with an example of a web application that displays a confirmation prompt, showing how initial tests can pass incorrectly when using asynchronous operations like delayed pop-ups. Bahmutov discusses various techniques to ensure tests wait for all assertions, including using spies, local variables, promises, and the popular cypress-wait-until plugin. The post introduces the cypress-expect-n-assertions plugin, which allows users to declare the expected number of assertions, ensuring tests only finish when this count is met, thus preventing premature test completion and ensuring accurate test results.