After Willi makes her first dive after her injury, Charley puts her cape on her and sets her shoes down. But he places her shoes in the wrong order - left shoe in front of her right foot and right shoe in front of her left foot. Anne Baxter had to do a cross-step to get her shoes on.
Joe didn't realize until shortly after Willie picked his pocket that his wallet was missing so would have not known it was Willie who stole it and therefore would not be able to pick her out in the crowd. Also when he confronts her, he would not have known where she hid his wallet.