If you're feeling a little daunted by the idea of randomised puzzle mode in this, don't worry, it's not all that different. You need to play randomised mode in order to obtain one of the achievements (going through the maze at the end of Selenitic without backtracking) and it may also help one of the currently bugged achievements pop off as well (seeing Bob the skeleton through the telescope in Mechanical.) Here's a list of everything that changes, all behind spoilers.

If you want a simple tl;dr answer: just make sure to check the tower for each area as you would in a normal playthrough and check the Selenitic book for the piano code.

• Clock Tower entrance puzzle
  
• Clock Tower puzzle
  
• Dates to input at the planetarium
  
• Picture code to raise the ship
  
• Safe code to raise the tree elevator
  
• Voltage amount to power Selenitic entrance
  
• Piano puzzle
  
• Fireplace code

• Telescope & Compass puzzle

• Code to leave the age

• Absolutely nothing.

• Door code
  
• Path through the sound maze

• Placement of the Red & Blue pages; They're in the same rooms, but in different areas of them.

• Noises for cardinal directions (Clink, Exhaust, Cowbell, Spin)
  
• Water drainer in Stoneship
  
• Island placement and puzzle solutions in Mechanical
  
• Number of the Fireplace code