But as you maybe guessed I have rather strong opinions about An Unexpected Journey (which I am talking about all over the internet) so I don't think that any one scene would have changed it for me really. :)
I think that if the eagles being called by Gandalf's moth was the only part of the "Out of the Fire and Into the Frying Pan" (or maybe more specifically "to escape goblins to be caught by wargs" haha) scene that I didn't like I wouldn't really care that much. Yeah, the moth is weird in Fellowship but it would be fine if it was there as the justification. But in the current context I think that it is just another example of the silly things that Jackson and co. do with the story to make it "fit" their version of Middle Earth, and the story they think they are supposed to be telling.
I almost might just be being a grump. haha. I totally didn't complain this much about LOTR when it came out (and I was just as big a Tolkien nerd 11 years ago... but maybe it had something to do with being 11 or whatever and also not having as much internet omnipresence to see thoughts shared and share mine. haha)
I actually don't think that the tone between An Unexpected Journey and LOTR is kept constant all that well. I think that I mentioned somewhere earlier in this thread (though perhaps it was somewhere else) that I think that the movie does a poor job being able to choose if it wants to be serious or childish. And I think that it has a lot of little childish things that would be fine in the form of a more "children's movie - book Hobbit-esque movie", but that I think make the tone of the current movie a bit silly and contradictory.
I think it was the wrong decision by Jackson and co. to make An Unexpected Journey in a way that directly ties it to LOTR (or so directly ties every aspect of it to LOTR), but once he made that decision I think that they didn't do a great job of really capitalizing on that.
While there is an attempt to retell the story in a more epic fashion there is this back and forth jostle between bookish-silliness (dwarves being ridiculous: see something like the party at Bilbo's house; or the storm giants; or the Great Goblin's death scene) and epic fantasy (the rallying speeches, all the gratuitous battles, the constant sense of danger and pursuit from Azog for the party). And I think that this makes the movie overall a bad one because it tries to do too many things and so fails at all of them.