The battle between Inu-Yashas' father and the demon Hyouga over the Sea of Japan was so fierce it caused the tremendous storm "Kamikaze" which thwarted the invasion of Japan by Hyouga and his human allies.
The US DVD includes an Inu-Yasha no Tsubo special as an extra. The Inu-Yasha no Tsubo segments typically run after episodes that air in Japan as a commericial break eyecatch. This special, however, introduces the lead characters and storylines of Inu-Yasha.
The apron that Kagome is wearing in the beginning when she is making lunch is a nod to one of Rumiko Takahashi's earlier works. The "Piyo Piyo" with the little chick (as in chicken) is the same thing that Kyoko Otonashi has on some of her clothing in the manga & anime Maison Ikkoku.