Being fascinated by glitches/beta, I just had to check it out, but I agree with Kazumi - it's nothing special. It would be if you could actually go there, but there's no collision, so you simply fall through the ground.
I'm not sure if it even is beta. It's probably just part of the background, judging by the simplistic shapes and textures. What I don't understand is why it's even there in the first place - it's barely visible from any normally accessible part of Link's house area.
BTW, Kazumi, what other beta areas are you talking about? I'd like to see them.