Gumshoe difficulty:
To unlock Gumshoe difficulty, beat Story mode on Detective difficulty.
Treasure Hunt mini-game:
To unlock the Treasure Hunt mini-game, beat Story mode on Detective difficulty.
Madame Fate messages:
Complete the investigations on Ron N. Hyde, Justine Time, and Manni Cotti to get a note with a riddle, and a choice between six rooms. Return to the study. The Crime Computer will alert you to something else in the room. Select the blue area at the filing cabinets to the right of the fireplace to find a crystal ball and Madame Fate the fortune teller. Tap on the Crystal Ball to get various messages from her.
The Hitchhiker’s Guide To The Galaxy easter egg:
At the start of the Astromalgy level you can see the number 42 which, according to The Hitchhiker’s Guide To The Galaxy, is the meaning of life, the universe, and everything.