1) Gandalf's letter which confirms Frodo's trusting of Strider. Though they did move my favorite line "...if by life or death I can save you, I will" to the Council of Elrond and it was much stronger there.
2) Merry and Pippen weren't 'accidental' companions, they were Frodo's best friends and would not let him go without them. That fits in later at the Council when they insist on joining the Fellowship.
3) (and getting ahead) Gimli, Celeborn and Galadriel's exchange when they first meet in Lothlorien. It shows the distrust between the Dwarves and Elves was both ways and how Galadriel started to heal the rift with her kind words and how Gimli starts to fall for her.
And I agree that Strider's "if by my life, or death, I can save you I will" - Is much stronger in Rivendell than it would have been at Bree.
And in my further reading tonight, I am nursing a theory that when Aragorn joins the company, that is when Frodo begins to begins to show leadership, because Aragorn treats him that way. And, perhaps, following Aragorn gives him confidence and security that he has not felt since they started, alone and guideless in the wild.
...and changed it to "if by my life or death I can help you," if memory serves. A favorite line of mine, as well.
Dan