RE: "I may not be a movie student.. but Shakespeare in Love comes to mind here.That was a "critical darling" of a movie too, wasn't it?"
I agree wholeheartedly. The oversight of the classic Saving Private Ryan in 1998 in favor of the cute but slight Shakespeare in Love was one of the Academy's biggest screw-ups in the 1990's. But like the man said at the end of Some Like It Hot "Well, nobody's perfect."
Now there was a comic genius!
"Shakespeare in Love" won because it was a movie about actors, and all about how wonderful it is to be an actor. And the actors branch is the largest segment of Academy voters. Naturally they loved it.