I disagree that Bombadil is necessary to the story. I mean, yes, he shows that SOMEBODY is not affected by the Ring, but why is this important? As Boromir points out, we see people giving up or refusing the Ring numerous times throughout the films. Surely that would suffice. Plus, Bombadil is an extremely unusual exception to a wide-encompassing rule.
Now sure, I like old Tom Bom jolly Tom as much as the next guy, but he flat out does not belong in these films, beyond the small tribute he gets from Treebeard in the TTT EE. We've been over this tons of times, so I won't list the reasons here.
EDIT: I'm not trying to sound arrogant, and rereading my post, I think I did sound like that more than a bit. I apologize. Sometimes I go overboard when trying to make my point. Please ignore my tone and just focus on the argument. Sorry.
And yes, Frodo seeing the Eye while wearing the Ring at the Prancing Pony is a big change with potentially far-reaching implications. So, that begs the question: Does it accomplish its purpose in the movie? And while we're at it, what IS its purpose in the movie? I'll sit back and let you guys answer that before I jump in.