I've completed the game, and have been given the option to start a new playthrough in "Hero Mode." I know that in Hero Mode, the damage dealt by all enemies is multiplied by four, but are there any differences other than that? For example, have any of the puzzles or boss fights been changed, or are there any exclusive secrets?
As far as gameplay is concerned, the only difference is the quadruple damage taken. Unlike Skyward Sword and Wind Waker's Hero Modes, you can find hearts by killing enemies or destroying the environment.
There is also an extra bit of exposition and a slightly modified scene in the ending
Ravio's diary can be read in the vacant house in Lorule, and Zelda and the sages accompany Link when he returns the Master Sword to its pedestal.
Source (Contains hidden spoilers)
Extra song, the flute boy plays the ballad of goddess.