If you are an architect or a builder - or you have manage or edit access to a grid - then you can set a due date for a checklist task.
With edit mode on, click on the clock icon to trigger the date picker. Select the due date you wish for that task, the picker will automatically close and the date set. To remove, click the clock icon again to trigger the date picker and then click on the Remove due date link below the calendar.
The latest due date applied to a task also displays below the related element's title, on the element thumbnail, the latest task due date in a stage displays below the stage title, and the latest task due date on the grid displays below the grid title.
The ability to overwrite and set the element, stage and grid due dates is a feature that is coming in the 2-4 weeks.