To block issues from being closed while there are still unchecked items in their Checklist, you can use the Block issue closing option. To enable it, go to Administration → Plugins → Checklists plugin: Configure, check Block issue closing and click Apply.
Note: Please note that this feature was added in version 3.1.11 of the Checklists plugin.
You are closing an issue when you change its Status to one that has an "Issue closed" mark. Issue statuses can be viewed and edited at Administration → Issue statuses.
If you attempt to close an issue with unchecked items in its Checklist while this feature is enabled, the issue will not be updated and you will get the following message: