After completing the first three levels, I manage to reach an isolated part of Kakariko Villiage (the SE corner with a chasm blocked off). After saving my game somewhere out of the villiage and loading it again, Link starts at the Kakariko villiage-underequiped to get out.
Bug with "Link's Birthday"
will most likely be fixed in the deluxe edition Mr. Z is creating.
You could try to use the whistle to get out, if you have that. (level 4)
If not... I think you're stuck then.
I managed to finish the game just now. In the middle of it, however, I discovered another bug, this one located in Ganon's Castle, that forced me to reset back to the dungeon entrance:
Ganon's Castle room 54 lacks a properly placed warp flag for those who try to enter via the stairs from the upper floor. If Link attempts to return back down to room 54 via the stairs, he is "stuck" (persumable in the upper lefthand corner) and the player would have to reset.