-The crimson loftwing may be the origin of the Hylian crest seen on the Hylian shield
-Demise is the source of all evil in the series (Ganon, Vaati, etc). This explains how Ganondorf escapes sunken Hyrule in Wind Waker, and how he appeared in Twiilight Princess. Expanding on that, if you have Fi give you info while to fight him she says that he has "conquered time" and "appears differently to everyone who sees him"
-It is heavily suggested that Link is the first hero and Zelda is the first Zelda
-The harp is the same one used by Sheik in Ocarina of Time
-The Triforce Crests that appear on Link, Zelda, and Ganondorf's hands in Twilight Princess are explained in this game. They are just marks of chosen ones or something to that effect.
-Zelda (and probably Link too) decide to remain on the surface to protect the Triforce, which would be the start of the Hylian royal family
-The Hylians and the kingdom of Hyrule likely get their name from Hylia
-The Triforce was found in the Silent Realm, which suggests that the Silent Realm may be the Sacred Realm
-The royal family of Hyrule are all reincarnations of Hylia
-The Sheikah serve the royal family of Hyrule because they were originally bound to serve the goddess
-Groose has golden eyes and red hair, which may mean he is the ancestor of the gerudo. Likewise, the Kikwi and Parella could be precursors to the Kokiri and Zora.
-Speculation on my part: Since it is heavily suggested that the Sealed Temple becomes the Temple of Time, and we already have a Temple of Time in this game, I think this game trys to explain how we have a Temple of Time is Castle Town in Ocarina, but it is in the forest in Twilight Princess. The desert temple becomes the one in Ocarina. The desert was the most advanced area, so when the Hylians repopulate the surface, there is a good chance their capital city would be there. The Sealed Temple would be the place in Twilight Princess. The only problem with this theory is that the Master Sword was left in the Sealed Temple, and not the Temple of Time in the desert.