Plot hole: The first time they communicate with the "entity" in the spaceship, they find a correspondence between numbers sent by the entity and letters of the alphabet. The entity presents itself as "Jerry". Later on, the entity tells Dustin Hoffman, "Stop calling me Jerry" - and then Dustin Hoffman realizes that the number-letter correspondence was wrong, and the actual name of the entity was "Harry". But if that is true, how could they have communicated without problems before? The very first word that the entity used was "hello", which would have to be displayed wrong, since it begins with an "h" and has an "e".