If I can take off the moderator hat for a moment and tell you a bit about my own thoughts on constructive criticism:
Most fan fic writers are amateurs. Some of them have never written anything before in their lives, and something about the inspiration they feel from a work leads them to write a fan fic. As a result, they are writing more from the love of the original work, than they are trying to polish something up for a readership, so "your results may vary" as far as quality goes.
Fan fiction writing is an act of appreciation by fans, and it is easy to fall into either a) unabashed praise and 'squee' as it is often called, or b) blanket disregard for the story if it does not the reader's "vision" of say, in this case, Jack and Ennis. There are also little sub-genres of work based upon how the subject is approached, what the pairing is, and if it is alternate-universe or uses the canon ending of the story.
The general suggestion we try to make here is to feel out the author if you wish to help them improve a story you enjoy but may contain some errors you notice. This is best done on their LJ if they have announced their story as "Feedback and comments welcome." That means the author is looking for suggestions.
As far as my own personal preferences, I am always grateful when someone has a point of fact to correct in my story: I lived through the early 1980's - but I did not live in Wyoming during the 80's, and so I have to do a certain amount of research, some of which is not authoritative, and some of it, while traveling as I am, if it is not available on the Net, I can't get to it. So this is where reader feedback of a constructive nature, can help. Many authors go through the helpful step of having a "beta reader" who makes suggestions and constructive comments/edits on a story before it gets put on LJ.
Our policy here is for the author to state whether constructive criticism is welcome on their individual story threads, but the most helpful way of course, is to send a pm and say "I had a few thoughts and some suggestions, would you like them?" that way the author knows you are trying to help, and may have some valuable assistance to give them - FOR FREE!
I once had a reader leave several comments on my LJ saying "Nobody in Wyoming says 'warsh' - you made a mistake there" and I replied that I was using the dialects as I found them in "Brokeback Mountain" - Ennis says 'warsh' twice and Jack says 'warsh' once, and they come from opposite ends of Wyoming. Since Annie Proulx lives there I took her word for the dialect. But the reader knew best and insisted I was wrong! That is not necessarily a constructive criticism, though, but more of an argument on what constituted "proper" dialect for the area.