Maria plays Beethoven's "Fur Elise" on the piano but it is clearly from the soundtrack. The notes are still playing even when her fingers are completely off the keyboard.
Two separate overcoats are used in different shots. Maria's overcoat is depicted in the film as having dual front to conceal her identity: airline hostess look on one side and casual pattern on the other side. The flipped over casual pattern side shown in the taxi changing scene has no pattern on the collar, whereas, the one she is wearing in the meet the student boyfriend (Gianni) scene has pattern on the collar.