Thanks --- I did know about that. For whatever reason, though, that doesn't appear to reliably bring back all notifications, only some of them. While I definitely could be wrong, I'm just about 100% certain that I've had notifications come and go that aren't to be found in the Notification Center afterward.

In the notifications settings/preferences, on a per-app basis, you can set whether notifications are displayed to allow banners, badges, and sounds. And you can turn on/off whether the notification posts to the lock screen, or stay in the notification center (swipe down on iOS, click the clock in the menu bar on OSX)

I'll have to look into this, but my experience has been that Notification Center: doesn't display everything; loses things on a whim; gives no way of recovering things, or displaying all things.

It definitely does. One reliable way I've noticed for this to happen is if you have the app that caused the notification open on another device. Presumably that app is then saying to the notifications system "don't worry, I've got this", but then that notification disappears on all devices.