Troubleshooting Custom Post Type Registration

Analyze the following WordPress code snippet (from my theme's `functions.php` file) which is intended to register a custom post type named 'my_custom_post'. Identify any potential errors or omissions that would prevent the post type from registering correctly. Provide specific recommendations for fixing these issues, including code examples if necessary. Also, check if the rewrite rules have been flushed to make the new custom post type work and tell me how to do so. Here is the code: [insert your `functions.php` code here].

I'm encountering a 404 error when trying to view single posts of my custom post type 'events'. I suspect there's an issue with the rewrite rules or the way I've defined the permalink structure for this post type. Here is the code I used to register the 'events' post type in my plugin: [insert your plugin code here]. Can you analyze this code and provide guidance on how to correctly set up the rewrite rules and permalink structure to resolve the 404 error? Include the specific steps to update the permalinks in the WordPress admin panel and verify that the rules work by using the 'Rewrite Rules Inspector' plugin.