In the case of an I.O.U., the sensible approach is to put the note in your wallet alongside your other banknotes and other things which technically count as, or can be redeemed for, money, like coupons and cards. Ideally the I.O.U. should be written by hand by the person who owes you, so the handwriting serves as authentication.

If only someone could invent monitors that sticky notes actually stucks...

Someone at work used to have a good portion of the screen covered in notes. In worst case she just used tape to get them to stick but most of them stuck without problem.

(CRT timeframe)

Yes, destroy the note immediately after or when doing the task.

Also you can keep a "queue" of tasks along the bottom/side of the monitor or maybe it ends up representing some sort of pipeline and before you know it you have your own personal kanban setup.