You can't click any of the options at the top while they are there though. And the little X that lets you close them all is often pushed way down below the screen.
On computer it's not that bad. On phone it blocks the entire screen until you use your jackal precision to press the tiny x's on every message.

I know. I'll look into making them so you can click on the topmenu while they're up, but as a quick fix before that happens, you can just refresh the page or click the logo to make them disappear.

To make sure none of the old notifications pop up, hover over your name in the top menu and select Updated Topics. Then you can mark all of those topics as read.