I keep a running document of bill pays. I add to it when one hasn't been received yet and delete that entry when I see it in my transaction history.

With gift cards, I liquidate them as soon as possible. I then put them into a pile before checking their balances online before putting them in a recycling pile.

With money orders, I deposit them using a mobile app and then keep them all in a secure place. My institutions have either next business day or immediate funds availability, so I just wait to make sure that the account is credited properly. I still keep the money order papers, though.