Your comments

I usually have preview set to nil (0 lines) because I prefer to see more notes in the main window. If I enter a search term a subset of found notes appears with the search term highlighted where it appears in the note title. That is fine, but what I would really like is what Thomas has indicated as his second thing (i.e., that on pressing Enter to open a found note all matches are highlighted, with F3 enabled to jump between the matches).
I couldn't reproduce this at first, but I have worked out that it was because initial focus was set to title rather than text.

What I would really like is to see the search term highlighted on pressing Enter from the title.
If this is too difficult to implement it would at least be useful if F3 picked up on the search term used to find the relevant notes. Then one could search for all notes with a given term; open one of the notes; and press F3 to jump to the search term within the note.