Bill Murray falling on his way out of the restaurant was unscripted and a genuine accident. (As evidenced by the reaction of the actor playing the waiter, and Murray's feet as he falls.) Apparently, it was due to the stairs still being wet, after splashing the waiter with water, that caused him to lose his footing.
Bill Murray and director Richard Donner reportedly did not enjoy working together, creating a lot of tension on the set. When asked by film critic Roger Ebert if he had any disagreements with Donner, Murray replied: "Only a few. Every single minute of the day. That could have been a really, really great movie. The script was so good. There's maybe one take in the final cut movie that is mine. We made it so fast, it was like doing a movie live. He kept telling me to do things louder, louder, louder. I think he was deaf."
When the Ghost of Christmas Present (Carol Kane) grabbed Bill Murray's lip, she tore it so badly that filming was halted for several days.
The leader of the street musicians insulted by Bill Murray is Paul Shaffer. The others are Miles Davis, David Sanborn, and Larry Carlton.
When Frank is startled by an actor who he thinks is the Ghost of Christmas Future, he elbows his secretary Grace in the face. That was real. Bill Murray really did hit Alfre Woodard by mistake.
Kathy Kinney: As the IBC nurse on the movie set, taking care of the censor after she is knocked out by a street light by one of the building crew.
Richard Donner: [poster] Keith Haring's "Free South Africa" poster is seen in a few background shots as it is in Lethal Weapon 2 (1989).
Richard Donner: [A Christmas Carol (1951)] As in Lethal Weapon (1987), the 1951 Alistair Sim version of Charles Dickens' A Christmas Carol is playing on a television in the background of one scene.
Richard Donner: [Christmas] One of several Donner movies set, in part or in whole, at Christmastime.