Well, if I recall correctly, even in the beginning, the power of the ring wasn't known.
Gandalf spent several years coming to the shire and leaving again, diving into all kinds of books, until he founds out.
Of course, he immediately recognizes it in the movie.
And when Bilbo used it as a "party trick" (my book knowledge is inadvertently mixed with movie knowledge, so sorry if I get things mixed up) and I don't think he was spotted by evil then. If so, he might have mentioned it to Frodo: "Here's this ring, but if you put it on, you see these creepy zombie kings of old."
With regards to my original spoiler: I know that the movie is old, but as he didn't seem to recognize Alan Rickman I wasn't sure whether he's seen it and didn't want to spoil the "big reveal".
Some movies are more spoiler dependent than others though.
But hey, here's another:
In the last season of Lost, they didn't successfully fix the timeline and live happy ever after, they're in some sort of purgatory/heaven