I have to agree with J. Hammond. Rei working for an undercover agency -- certainly a government agency -- is not believable. But there are other objections, and some plusses.
Good Things: The story is interesting, and much less hackneyed than most mystery novels. Also, as usual, the information / culture about Japan is wonderful. I much enjoyed all the information about the department store, the needle blessing, etc.
Bad Things: I agree with Hammond: lose the labels. They make Rei seem shallow and pretentious, like a chick in bad chick lit. The occasional designer reference as appropriate to the story is OK, but the REI I know would not be plugging "comme des garcons". She'd be wearing jeans by someone normal, like JCrew, LLBean, etc.
Another bad thing: Even without the label-dropping, she is starting to seem really shallow to me. There is occasional lip service to how Hugh "broke her heart" but no real sense of missing him. Really! They were engaged! She ought to be remembering him and trying to get him to forgive her. No one gets over a REAL serious romance of long standing that fast. And she spends the book wanting to [bleep] her new boss. Come ON! This is not the Rei I used to like.
Also, she seems not to remember that SHE cheated on Hugh. No, she says He broke Her heart. A little honesty and regret would be nice.
Finally, I miss the antiques. Bring back the antiques and bring back Hugh. At least make Rei's emotional life a little more mature.