Yes, very difficult to apply labels such as "important work". I do agree that it has been very successful in bringing to light a chapter of American foreign policy involvement which has been hidden from sight, and it does capture the reality of the Vietnam war from the point of view of the American soldiers involved. I guess as #3 establishes the true test will be if it is being read and studied a 100 years from now.
I agree that it's impossible to tell if it's an "important" work; in my mind, O'Brien's "In the Lake of the Woods" will probably be read longer than "Things." I don't think it's the content/topic that make this book memorable; after all, there have been many war books that present the misery of war; "All Quiet on the Western Front" may be the best of these. What O'Brien does well is create real imaginary people (I think he'd like that given his distinction between story truth and happening truth). The focus on each individual as some of them wander from story to story helps us feel for the little things that make up their lives. We come close to men suffering; the immediate cause is the war, but to me the book is not about the war, but about the people, and O'Briens ability to bring us into the life of the suffers is what will contribute to this book's long life.
The Things They Carried came out in 1986 originally, at a time when the Vietnam War had been over for only 13 years, and Vietnam had been lost for only 11. Large numbers of "Boat people", Vietnamese refugees, had come to the US during this time. I remember this time because I was in high school. People didn't talk about Vietnam that much. It was as if it was a subject they wanted to avoid, or just forget about it. Such an ugly chapter in history that many just wanted to pretend it didn't happen, or didn't know how to talk about it. O'Brien's novel in 1986 and the construction of the Vietnam Memorial Wall in DC in 1982 broke the silence and the ice about this topic in an important way that allowed us to begin healing as a country.
I would not exactly call it an important work of American literature. It is far too early to tell how significant it will be. But from initial acclaim that it has received already, perhaps it can be in a hundred years time from now. Until then, and other books of war come out, maybe it will move up the ladder to reach canonical status.