Well, obviously I disagree re: The Exorcist, but I'll spare you my Mount Everest of reasons, except to say I think that film has endured far more than The Sting (much as I love The Sting, don't get me wrong).
Also, I don't believe The Truman Show should have lost to Saving Private Ryan. The film has an amazing opening (on Omaha beach) but nothing else quite matches that (though it's still a fine film), and I think the prologue and epilogue are largely superfluous. By contrast, The Truman Show is riveting from start to finish, without an ounce of fat. I would have given Spielberg the Best Director Oscar (which he won), purely for the opening (and obviously that section proved so influential it pretty much changed the way war films were made (see Black Hawk Down, The Hurt Locker, Hacksaw Ridge, etc, etc). But as a film overall, The Truman Show is better in my not remotely humble opinion.
Regarding the Titanic/LA Confidential business, I confess I'm a bit torn. At the time, I thought LA Confidential ought to have won, but in the intervening years, I've become less convinced of this. Cameron's film may be a blunt instrument born of raw ambition, but it's a hugely effective and satisfying one. Yes, the romance is one-dimensional, but it works, and so do the disaster movie elements, especially on a huge cinema screen. On the other hand, LA Confidential is still a cracking thriller with some great performances. So in short, I'm on the fence with that one. :)