It appears that you can conduct a word or phrase search of the notes one person, but you can't search for a phrase among all the notes. Am I correct? Thanks.
You are incorrect. In the main window click on the Tag by Matching button. Enter the phrase opposite Notes Contain. All people whose notes contain that phrase will be tagged. Then you can look at any one and use command-F and command-G to find exactly where the phrase occurs.
I suggest you read Tag menu > Tag by Matching in the Reference Guide to learn about the real power of Tag by Matching.