The song "White Christmas" originally appeared in the 1942 movie "Holiday Inn," starring Bing Crosby alongside Fred Astaire, although the song is usually referenced back to this movie.
In the scene where Bing Crosby and Danny Kaye are escaping the club where the sisters are performing, you see Bing Crosby hail a cab. Not withstanding that there happens to be a cab in the alley, but moreover, when Bing "whistles" you can here that he wasn't able to do it. It comes out as a "flub" sound. Not really a mistake, but kinda funny.
Ever wonder why Vera-Ellen is always shown in the movie wearing a high collar dress/shirt/pajama top/etc.? She was suffering from premature aging effects (she was only 33 at the time) from what is believed to have been anorexia. It showed predominantly in her chest and neck - hence, the desire for her to have her neck covered.