Follow the below checklist in order to test a WordPress plugin:
- Create the test cases on the basis of requirement doc and test all the test cases with every major release. Use this template to maintain test cases
- Test plugin with default theme first. All functionalities should work with the default theme
- Test with 10 popular themes.
- Test with other popular plugins and the required plugin if any
- While testing keep an eye on error log, keep the debug log on, Refer https://codex.wordpress.org/Debugging_in_WordPress
- Prepare your plugin for WordPress next release by testing with WP RC or beta. You can also use https://wordpress.org/plugins/wordpress-beta-tester/