In a series, one word will often refer to all the items in the series. Consider this sentence:
"The knight had strong armour, shield, and lance." Strong refers to all three equally.
"It is vital for a viewer of this movie to listen for its main character's underlying position, contrast it with those of the other characters, and ultimately determine which view is true."
In your sentence, removing the second and third "to" while not incorrect, makes it more difficult for the reader to pick up the beginning of each listed item. Especially because each item is complex. So repeating the "to" when using infinitives in a complex series makes the sentence clearer. 300 Days to better writing