This has a bit too much exposition. The readers already know that Inuyasha's father was a full demon, that he was shot through with an arrow, etc. etc. If you need to talk about these things, then focus more on Kazumi's reactions and thoughts than on the facts themselves.
Typos et al. (Non-nitpickers, ye be warned!):
"wished to thinking" (wished to think)
"When are we going to call the police," (?)
"You see," she said, handing him the cup. "I had a visitor last night." (only needs the last period)
(Numbers that take two words or fewer to say, like five hundred, should be written as words.)
Thanks for the review! This one was actually my very first Inuyasha fic from a few years back. :) One quick note: I write my stories using Associated Press style, since my primary profession is a journalist. In AP style, the numbers zero through nine are written as words and then in most other cases, 10 on above is written in numeric form. It's a style that I choose to keep in my stories.