It is a bit lucky for Bilbo to actually find the dwarves and Gandalf after his escape from the goblins, isn't it? Although, depending on the lay of the land, it might tend to channel a person towards that spot, I cannot say for sure.
Dori ends up performing almost the same role in this chapter as in the previous one; Hobbit-porter. One does wonder, however, why the eagles managed to spot and grab every one of the dwarves, but missed Bilbo. Either he is a good deal less noticeable than they are, or in fact there would have been another eagle coming for Bilbo, except since he grabbed onto Dori's legs why not let him go that way.
Gandalf started the fires, and a couple chapters back he was able to extinguish every fire in the Great Goblin's hall, but here he is choking in the smoke just like everyone else. Aside from the "it's convenient for the plot" possibility, I can think of two reasons why he does not just use his fire-magic to extinguish the fire. First, perhaps after a long day or two of running, fighting, casting spells, running, fighting, hiking, etc. he just doesn't have enough oomph left to do it. Second, perhaps he could do it, but the goblins know how to start fires again, and now that they have the idea they will happily keep restarting the fires until he cannot stop them. So perhaps he could, but knows it would be pointless, and decides to save his energy for a last attempt at driving them away in fear.
The narrator says that if Gandalf had actually jumped down into the clearing (as he was preparing to do), that was full of goblins, it would have been the end of him. It is hard to imagine Gandalf (even Gandalf the Grey) meeting his end at the hands of goblins, but in sufficient quantity I suppose they could overwhelm him with numbers. Especially given, as mentioned before, that he was probably pretty worn down already.
I have to imagine, though, that there would be at least some chance that they would have been a bit intimidated by the presence of an angry (and Orcrist-armed) wizard in their midst, and perhaps look a bit from side to side as if to say, "wizard, very dangerous, you go first". I picture Thorin jumping down to help out, also, and then the other dwarves trying as well, and it would all end in a pyrrhic victory for the goblins, at best. But, not a great story.
Even if I were in a tree with goblins and wargs below, and choking on smoke, I wonder if I would have had a bit of reluctance to get up in snatching range of giant eagles who I knew nothing about. Who says they're not going to treat you the same way a bird of prey treats most of what it snatches? One eagle even says that Bilbo resembles a rabbit. I don't suppose a giant eagle can stay fed on rabbits, by the way, so one wonders that they eat. Goblins? There could be a reason they hate the eagles so much; perhaps it is similar to why certain monkeys don't like regular eagles.
If you really try to visualize the flight scenes, one can get a bit queasy, just like Bilbo.
Bilbo isn't able to help out much with cooking the rabbit that the eagles bring them, by the way, as it says he is accustomed to cooking rabbit that is already cleaned and ready. It is another glimpse of how Bilbo's journey eastwards is almost like a journey back in time, from Georgian Great Britain to medieval England. Butchers do not sell you meat that is already shorn of fur or feather, here, you have to do that bit yourself. I am realizing that some parts of "The Hobbit" are a bit like "A Connecticut Yankee in King Arthur's Court", in this way.
Chapter 7