Each puzzle presented to Luke or Professor Layton is worth a number of Picarats. The more Picarats a puzzle is worth, the harder the puzzle will be to solve. Ingrid hints at the start of the game that collecting Picarats will lead to something good.
Once you've beaten the game and saved after the credit, "Top Secret" will be unlocked under Bonuses. Depending on the amount of Picarats you've collected after solving puzzles you can get access to different content. The maximum Picarats you can get is 5312 in the US-Version / 5302 in EU-version, since there are 4 puzzles that give you different amount of Picarats. These are:
But you can also get everything even if you have the lowest possible Picarats if you solve every puzzle.
You can check every characters which pop up in the game here. Some information in it isn't found everywhere. Along with the profiles there is also sprite shown from every characters.
In this section you got to see 20 screenshots from within the game like a screen of Lady Dahlia with small Flora and Matthew to the repairing broken Pauly, but these are all screens you already saw in the game.
In here you can listen to 19 different music that are played in the game.
In another section you can listen to voices spoken by Professor Layton and Luke in the game.
In here you can rewatching the movies again from 16 different movies from Bruno escaping from Professor Layton and Luke to the ending.
For that you need the following game Professor Layton and the Diabolical Box to complete it and add the code found there here to view the content.