Hello! 
I’ve noticed already that the search will be improved. Let me add some quick thoughts and reasonable feature requests all around searching. My assumption is that the user want simple-to-use and intuitive functions. I have some ideas more, but here first of all the more basic one:
a) Under notes in the left sidebar you will find some sub-nodes like “today”, “not-tagged”, “todo” and “locked”. Why don’t you place these entries and some more (f.e. “attachments”, “task”, “yesterday”) in a drop-down-field or pop-up that is placed directly beside of the search bar? The advantage is evident: The current entries in the side bar just filter all notes, but if a tag is chosen in the sidebar you have to write an @-expression in the searchbar. With a drop-down field or a popup you could search targeted either inside all notes or inside of a certain tag folder and that without using search expressions (side-effect: you can keep he sidebar clean because the notes-node wouldn’t contain sub-nodes anymore)
b) Allow multiple selections inside of that drop-down field or pop up. If you don’t know what i mean just take a look in apple mail and how it offers the opportunity to select more than one entry for filtering the mails. That would farther decrease the usage of search expressions in the search bar by the usage of simple clicks.
c) Nevertheless it will happen that you need to use the searchbar with search expressions.Wouldn’t then the pop up field - i talked in the latter two points - be the ideal place to store such a search expression from the search bar and to assign it with a pretty name?