I don't think that's how it's supposed to work.
The notifications there at the top (say you have 10 new likes) when clicked takes you to a list of liked posts. You can click on any one of them and then just continue browsing, and they should all be marked as viewed. That's how it's "supposed" to work, and how it seems to work on my profile.
If it doesn't let me know and I'll look into it.