A greater mistake. Not only Jackson is not coherent with Tolkien, but also is uncoherent with himself!
Aragorn, in the films, receives Anduril after the battle at Helm, but he already bears it before...
When the fellowship is trying to pass through the Redhorn, there is a moment when Frodo falls and losses the ring. Boromir takes it from the snow and Aragorn orders him to return it to the halfling. During this, we can see Aragorn's hand very near to his sword, as a sign that he will use it if needed. If you look well at the sword, you will see that it is Narsil/Anduril.
Oops, maybe a little out of topic, but you might find this link interesting:
PS: For those who are curios, my true name is Eduard, that comes from anglosaxon Edward. Its meaning is "keeper of the richness and prosperity" or, more freely translated "keeper of earth". Heren means keeper in quenya, and varda is earth. Putting it together and masculinize the name, Herenvardo is a translation of my name to elvish.
Many name translations available at [elvish.org...]