Early in the film's pre-production stages, Dustin Hoffman and Anne Bancroft were strongly considered for the roles of Beau Burroughs and Katherine Richelieu. But when Bancroft died and Hoffman had filming commitments for several other projects, the roles were given to Kevin Costner and Shirley MacLaine.
Along with President Bill Clinton and Fidel Castro, the picture on the far left is Beau (Kevin Costner) with Rob Reiner (the director). Hugh M. Hefner was originally supposed to be pictured, but Hefner objected at the last minute; Reiner was added in digitally.
When Sarah and her father are in the kitchen, he sets a mug of tea in front of her. She reaches for the handle around the front of the mug, but then in the next shot, she's turning the mug from behind it.