Alan Rickman was handpicked to play Snape by J.K. Rowling, and received special instructions from her about the character. Rowling even provided him with vital details of Snape's backstory, not revealed until the final novel.
Richard Harris, who had been acting for more than forty years by the time this movie entered production, stated that he had never been involved with a cast that was as close as this one.
The child actors and actresses would do their actual schoolwork in the movie, to make the school setting more real.
Richard Harris had trouble remembering his lines, and Daniel Radcliffe would ask him to help with running his lines, just to give Harris more practice.
The Hogwarts' motto, "Draco dormiens nunquam titillandus", means "never tickle a sleeping dragon".