Is the Movie Correct?

The movie has many different take-offs from the original version of Richard III by William Shakespeare. One detail that is different is the scene when Richard tries to trick the men that he doesn't want the crown. He is supposed to come out with two priests on either side due to the fact that he was in "prayer." However, in the movie he just comes out with a prayer book and no priests. The book isn't even a prayer book, it is a novel that the cover is taken off. Also, when one of the characters is killed he is killed through the bed while with a woman. Also, another difference is that the princes never make fun of Richard. In the book, the princes sarcastically make fun and tease Richard; however, in the movie they get into the car and no jokes are tossed around.