This is a point about the series as a whole and movies in general, really; but I think of it now because I remember Éomer's introduction in the book and I loved it.
I don't think the characters are introduced properly. For quite a while, the audience is left wondering 'Who's that?' and then maybe 20 minutes later someone will randomly mention his/her name. Same went for Boromir in FotR. I want the characters to greet the audience.
Anyway, I positively adore the shot of Barad-dur at the start of this sequence. It takes my breath away every time. If I ever have a castle I want it to look as terrifying as that. I wonder how it looks on a sunny Spring morn, though.