It depends on how hard she was "looking" at it. If she was in agony, and had to have it. Then it might not be a bad present. The coat won't mean anything to her, but the fact that you remembered she wanted it will.
If it was just a "Oh, that's a nice coat"... then blow it off, and just take her out for a nice evening. It will be appreciated more than the coat. We all know that women fawn over the dumbest sh|t and then forget about it completely a week later.
If you do buy it; don't give it as an "anniversary/whatever present" that's lame & will set the bar too high for later gifts.
I generally avoid buying anything clothing related for women. It always ends up being moth food in the closet (There goes my new video card

).