The ability to use search operators to search through notes could be used to more effectively and quickly locate specific notes, especially on cases where there are hundreds/thousands of notes. For example, an operator that limits the search results to only notes written after or before a specific date would make it so you don't have to scroll down through years of notes. Or, being able to limit search results by what user wrote the note, being able to exclude notes containing a specific phrase from the search results.
Another example would be an ability to limit the search results by using " " as a search operator. For example, searching "property damage" would only return results including the entire phrase exactly as specified by the operator instead of every instance of the word "property" or "damage".