When your hero reaches level 40, you could be treated to a special dialogue session, is there a way to view this again?
As of version 1.6.0, you can now view the level 40 5☆ unit dialogue again! By going to Settings, you you can select the Hero Catalog to view your collected units and see their dialogue for being summoned as well as their level 40 5☆ dialogue.
The heroes with glowing backgrounds are the ones that have their level 40 5☆ dialogue available to view.
A compendium of all of these "level 40 dialogues" can be found here (the character names are the Japanese names, though, so Aqua = Azura, etc.).