You can use the document reminders functionality to set these up on an ad hoc basis, via the Info tab of Document Preview.
Alternatively, you can use a workflow step to automatically setup reminders on documents.
Separately from the use of document reminders, if you are queuing these reminders/actions off an existing date stored in an attribute, you could setup a report to include those documents and schedule that report to be sent, if someone needs to be
There is no ability to confirm a standard document reminder as complete. If you need a process to do this and track from an audit perspective, it may be worth setting up a small workflow specifically for this purpose and having that triggered by a smart rule.