Here's my take. "Michael Moore Hates America" is a subjective statement. People who support him won't agree with it.
Providing a short article or two that objectively shows him to be a liar can actually reach some people on the other side. It pushes the issue to one of credibility and truthfulness, and away from one of political disagreement.
Instead of walking out of the movie, seeing the signs, and thinking, "Oh, they're just saying that because he busted Bush", they'll be thinking, "hmmm... so now I KNOW that these two things were lies, I wonder if ANY of this film is true."
Where do you get the idea that a movie goer would ever want to read a position paper or MORE than one line?
Michael Moore hates America
That is all you need on a sign and tons of people seeing that will be uncomfortable and won't go to that.
You are not going to get the red eyed liberals to shy away or listen to you.
If they read it, that is. Most of the idiots who will pay good money to see this POS already have their minds made up. They won't read anything that threatens to refute Moore's lies.
But it's still a good idea to try. The only thing I would suggest different is to pass out the flyers before the movie--especially if there are lines of bored ticket buyers. Besides, it would be better to get the facts out before movie goers have had their brains worked over by the movie.