The scene where Sam, Lucy, and Sam's friends are walking across the street with the balloons is a tribute to famous photograph of The Beatles crossing the street from the cover of "Abbey Road".
There was originally to be a line where Brad (Brad Silverman) asks Rita (Michelle Pfeiffer) "Are you wearing a Wonder Bra, because you look wonderful today...". Silverman thought the line was offensive to David E. Kelley (Pfeiffer's husband) and refused to say it.
Sean Penn wanted the soundtrack to be all Beatles music, but was unable to get the rights, so he asked various artists to cover the Beatles songs he wanted to use. And in order for the re-recorded music to fit into the movie, each of the artists had to use the same tempo as the original Beatles songs.
Dakota Fanning's character is named Lucy Diamond from The Beatles song "Lucy in the Sky with Diamonds". Michelle Pfeiffer's character's name is Rita Harrison, from the song "Lovely Rita" and the last name of Beatle George Harrison.