We don't display notes for several reasons. First is that they can be very long, so there is not really any room (especially on an iPhone) and second, they can have Carriage Returns (CR) in the text and that cannot be displayed on the line.
That being said, do you create a new Task for each of these that has it's own ticket # or do you reuse the Tasks? The reason I ask is that you can turn On/Off certain labels on the main Time Entry page. Setup -> General -> Entry Subtitle. You could put the ticket # in the Task Code field and turn it on, and you can even move it to the top so that it lists first.
You can also Search for things. Just pull down on the Time Entries page to reveal the Search box.