As FoolRunnning said, there is no simple way to bulk mark read the notes. However, if you have the notes list open, with the list filtered to “unread” then simply clicking in a note will cause it to be read. You should be able to work through notes that have been resolved pretty quickly by looking at the resolved icon in the left corner and clicking the note.
Once you click the next note the first note should disappear from the list. As a hint, if you click the second note in the list (or other note further down) it will move to the top so that if you click again you will be clicking in a new note and they just keep disappearing.
Video on rapid marking of unread messages