"Falsies" isn't a term used much nowadays. It was more common in the 1950s and before. Falsies are padding that women put in their bras to make their breasts look bigger.

I remember that! That's from "The Catcher in the Rye!" I wasn't certain about "pointed all over the place" when I read that book in high school and I'm not certain I understand it now, but this is what I think. In the 1950s bras and bathing suits usually were designed with a flat, heavy piece that was designed to hide the shape of the nipple. I think Holden Caulfield is saying that not only did this woman wear falsies to make her breasts look larger, but that they had a someone conical or pointed shape. This was considered very daring.