At the Teeth of Mordor
 

When Aragorn stands before the host of Mordor at the Black Gate, (at least in the movie) Sauron seems to be calling out to him....what the heck is our Dark King saying?!

Yes this was purely from the movies...perhaps it was an attempt at dramatization? :rolleyes:

Anyway, when Aragorn looks at the Eye, the Eye says 'Aragorn. Elessar;' that's all.

I agree...I always found it funny that Gandalf makes some Jedi style hand move after Aragorn turns around...and then of course the famous "For Frodo!" line.
Anyway, there is no way Aragorn could have seen Barad-dur from the Black Gate anyway, that's just changed in the movies to make it look better.
However, we do see that Sauron is summoned to come to the Black Gate as well, so this "Aragorn, Elessar" thing might be seen as a reply to that challenge.

Yes, I remember that. They scrapped the whole fight scene between Aragorn and Sauron, though. Instead of Sauron, it was a great big Olog-Hai stomping him.