The language that Swivel Tongue (Cliff Nazarro) uses was called "double talk" and was a popular fad during WW2.
In reference to the Cole Porter song "Night and Day" sung by Fred Astaire in The Gay Divorcee (1934), Porter ended "The Wedding Cake Walk" with the phrase "night and day." He asked permission from RKO to quote the line.
This was the first of two musicals Fred Astaire made back-to-back with Rita Hayworth. The other was next year's You Were Never Lovelier (1942).
The uncredited woman who sings "Wedding Cake Walk" is Martha Tilton. A popular singer in the big band era, she was nicknamed the Liltin' Tilton.