Heavy on the fiction, weak on the science. This makes the human race look incredibly stupid. They are completely guessing at what the aliens are saying. They have no proof at all. Seems to me, beings would be able to decipher our simple symbols before we could make any progress with theirs, duh! They mastered space travel didn't they?
Also, in order to communicate in a first contact situation would be to use symbols that we both have in common, and the only thing that we could have in common would be the elements of the periodic table. Quantum physics would be the only way to communicate initially.
Last point, and this goes along with the first point. They mastered space travel, obviously superior. Wouldn't they have first contact protocols ready, before they actually land. Why come and just sit there looking stupid? Awaiting a primitive species to figure you out. Wouldn't they at least take the lead, not let some dumb college teacher to bumble things up.
I'm sorry but this movie is just plain dumb. At least the science portion of it is.