Completing a Journal's list will adorn said list's menu button with a small medal.
Features of the Journal
The biggest feature is the Mii Cast, which allows the player to reassign a Mii to any of the NPCs which have been met so far. The NPC must have been introduced or prompted to allow them to be recast, except for the random Mii characters in the Travelers' Hub, where this rule does not apply.
The Monsters menu allows the player to review any monster that has been defeated, see their kill count and "poke" them. This will play their animations in order of "attack" to "specials" to "damaged" to any enemy-specific animations like eating Miis (Flytraps, Burgers), vanishing (Snurps) or inhaling air (Frogs).
Heroes in the Inn can pose with any monster and enemies with a Mii's face can have a posing hero's face copied onto it. Enemies can also be viewed in detail via "Take a closer look" option.
All collected grub can be viewed here, with a description. As a fun extra, tapping or pressing a button while over a food will "eat" it. Doing it enough times will remove the food and play a chime; the food will reappear when re-selected.
All weapons that have been held by any party Mii will be viewble in this menu. The weapons are sorted by class and selecting one allows the player to examine it from almost all angles.
The Clothes section is layed out exactly like the Weapons one, with some differences. All color variations of clothes (except starter gear, which is always red) can be seen and the camera in Examine mode cannot look down or up.
The Music section lists all music that has been listened to. Music can be replayed. While playing, it can be paused or restarted and random party Miis (up to four) will dance on the top screen.