Either CTRL click or right click on a day and choose "done" from the context menu and it places a large X on the day and grays out everything in it...or no X, but clicking on done at least turns all events grayscale - that would go a long way to making it easy to see, at a glance, exactly where you are in your month, and see what's been finished already.
One of the cool advantages of a physical calendar is the ability to easily mark entire days as done and I feel like this would be well-received in Lightning as well.