One thing to check is to make sure you are using the most updated version of the base MyBookProgress plugin (you can check to see if updates are available by going in your website dashboard menu to Plugins > MyBookProgress. If an update is available, there will be a notation to that effect next to the plugin's name).
If you're having problems getting your Mailchimp API key to validate: Remember also to try clicking the little refresh button immediately to the right of the API key box after you've pasted your Mailchimp API key. That button "tests" the API key to see if it is a valid one.
If you did click the refresh button but still received an error message, you should check to make sure there are no extra spaces entered before, after, or in the middle of the API key. Even one extra space will render the entire key as "invalid" in the system.
If you've tried all the above and are still having problems, please let our support team know.