In “Bogwarts Faculties” mine, in the kitchen before entering the Hufflehog Common Room: placing the three pumpkins on the vines rewards you with a region-dependent experience bonus. In the Hufflehog Common Room, putting the blue shells on the vines rewards one gem.
On the way to the Owlbeak Common Room, placing the record on the gramophone rewards experience. In the Owlbeak Common Room, placing the blue potion vials on the blue pain splotches rewards a gem.
In the Batwingus Common Room, placing the green potion vials on the moss rewards a gem.
In “Bogwarts in Danger”, the reward below by @BlameTheParrot. Also, in the Potions Lab, move the three barrels across the room to the green goo splotches for gems.
There are a few other “main story” secret prizes - @DiggysAdventureHelp has posted the videos for solving these now in his video guide compilation.