A much requested feature to be able to see previously completed and future checklists has been implemented in a new release. There is now Daily Operations calendar functionality to navigate to previous dates and see submissions for that date.
Navigate to Checklists and then go to the Store Page. You'll see the Calendar above the Ops checklists for that store.
The calendar view will show a history of submissions over time as well as checklists coming due based on their individual schedules.