As much as I love Celeste Holm...
I really think Dorothy should have won the Oscar that year. She had the more challenging part by far. Celeste's character was far more likable, and Dorothy had the thankless job of playing a rather irritating character - Kathy is a snob, who's trying in her own snobby way to not be a snob.
In terms of acting, Dorothy's role was much harder, and she nailed it. Anne is the nice girl who sees the way things should be. Kathy is much more complicated (especially given the strange ending that she's the one who gets the guy at the end). I could picture several actresses who could have played Anne just as well, but I could never picture anyone but Dorothy as Kathy.
I don't care about money. I just want to be wonderful. - Marilyn Monroe