Becoming invisible and big flying eagles

Rating: Null/10 (23 December 2013)

Maybe some of you out there who have read the books can explain this to me.
In the first Hobbit movie, there's a scene where the company is cornered at the edge of a cliff, so Gandalf finds this butterfly and it flies away and next thing you know, a bunch of eagles come save the day. Not only that, they fly them even closer to their destination so they don't have to walk their helpless selves over dangerous terrain.
All I could think of from thereon is: why not just take the eagle express to Erebor?? If there is some explanation in the book that might explain why the safest (or safer) and quicker option isn't taken, I'd like to hear it.
Other thing is when Bilbo is up in the dragon's lair trying to get the white stone, why not just use the awesome invisible ring to walk away with it when he sees it? I mean, it's gotten his ass out of dire situations a whole bunch of times, and when he's now faced with a fire-breathing gigantic dragon, he first wakes the dragon, then uses the ring just to hide away, and then takes it off the rest of the time. Am I missing something or do some things just neglect logic in this story??