From http://www.glyphweb.com/arda/movie.html:

As Frodo and Sam are leaving the Shire, just before they meet Merry and Pippin, we see them walking through a field of corn. When Tolkien writes about 'corn', though, he uses the word in its British sense, meaning a crop like wheat. The corn we see on the screen, though, is maize, a plant native to the Americas that couldn't possibly have existed in Middle-earth (which represents the lands that now lie east of the Atlantic Ocean). There's a similar slip later in the movie where Merry and Pippin cook tomatoes - there were no tomatoes in Middle-earth, either, for just the same reason.

That's pretty hair-splitty... considering that a big part of the setting, in The Hobbit as well, includes pipe-smoking. In Tolkien's forward in FOTR, he spends a few paragraphs explaining that it was hobbits who invented smoking "pipeweed", which is obviously tobacco (a New World plant). And this Hobbit habit was picked up and enjoyed by Dúnedain men (rangers) and dwarves and wizards especially, all longer-lived folk who never got cancer apparently. Now that's fantasy.