After turning on the game, press Start quickly to get to the menu screen. Press Up to get to the Options screen, then hit A. As soon as that screen appears, press B to return to the menu select screen. Press B quickly again to return to the game intro screen. This time, the opening video should be different than it originally is.
Call Epona and ride to Milk Road. Find the Owl Statue and assign the Zora Mask to a C-Button, then save while still on Epona. Start the game again and you should find yourself still on Epona. Press the C-Button you equiped the Zora Mask to. You should change into Zora Link and not able to fit on your horse. Press the analog stick forward to find that you can use Epona without having Link on her. You can do this on anyday. Also you can do this at Southern Swamp too. *Note: You will be stuck in Milk Road or Southern Swamp after you do this trick.*
To upgrade the Bomb Bag. You must do the following things.
There is a dirt hole on the southeast wall of the outside of Clock Town. Catch a bug in a bottle, then release it near the hole. The bug will climb into the hole and reward you with a Rupee for your efforts.
When you fight the Ikana King, Igos du Ikana, wear the Captain's Hat. You'll trick the king into thinking that you're Captain Keeta, which will launch a brief cutscene.