The price of apathy is blood - the accumulation of evil in Mordor was characterized as being attributable to man's inattentiveness.
Something that was left out of the movie which was quite important, was the "Scourage of the Shire." Remember in Fellowship, the scene in the Tavern, where one Hobbit states more or less, that if you don't go looking for trouble, no trouble will come to you. The Scourage of the Shire shows that there's no place to hide from evil. That even if you don't want to get involved, too bad... You will be involved whether you want to be or not.
Strength of character trumps physical strength - Only the virtuous Frodo was capable of carrying the ring, even though he was physically perhaps the weakest.
Another important point was that Frodo wasn't the real hero... It was Sam. It was Sam that got Frodo to where he needed to go, and he never abandoned Frodo. In fact, as true as Frodo was, in the end, he faltered, and would have failed, had it not been for Gollum. Showing that even the most stout of heart can (and will fail) against evil, unless you've got help, and a lot of luck.
Mark