I think the Randall situation just has to be left up to individual interpretation. People will always read this scene in different ways. I'm personally still convinced that Jack is asking Randall to dance (in a non-serious way) but that he's assuming that everyone else at the table will presume that he's asking LaShawn. He knows they will assume this, so he takes this opportunity to be playful and also a bit spiteful of Lureen. He can make eye contact with Randall and still have people (people at the table and the viewing audience) assume that he's looking at LaShawn since they're both sitting at relatively the same angle next to Jack. He can look past her, essentially, and at Randall. He then does shift his eyes to look at her once she replies.
I think it's important that he locks eyes with Randall during the conversation at the table, then during the "want to dance?" moment and then again when he stands up with LaShawn. He's sort of speaking in code to Randall here and trying to figure him out... I think this scene is meant to be all about what we'd call "gaydar" these days. Sometimes you have to do strange and bold things to determine whether or not a person might be gay or open to flirting (it's really not some kind of 6th sense). I think, like some of you, that this is what leads to Randall's offer on the bench.
Last week when I watched BBM with a friend (it was her first viewing) she just freaked out at the Randall scene. And, I don't quite know why it struck such a nerve with her. She said something like... "oh no, this guy is trouble."

By the way, why doesn't Randall ask Lureen to dance after Jack and LaShawn get up? I've always thought that was sort of rude of him.
That's how I interpret it, too. I mean the way you do, Amanda, not the way your friend did. (Hunh?! Randall seems like a nice enough guy!) Though I've also thought it was a bit rude of him not to ask Lureen. And she seems slightly miffed -- though mainly at Jack, probably.
As for Jack and Randall's eye contact, now that I think about it, can't you actually see Jack's eyes slide from Randall to LaShawn after LaShawn -- naturally assuming he was asking her, which of course he officially was, while taking the opportunity to flirt with Randall -- chirps, "Why yes! I would!"?
This is kind of the opposite of the Jimbo scene, where Jack's eye contact pisses Jimbo off. The first time I saw it, I didn't get either why Jimbo got mad, nor how Randall knew to extend the cabin offer. Duh! Next time I figured out to watch the eyes.
I love this scene: the eye contact, LaShawn's entertaining blabbing, Jack's cute smile at LaShawn's blabbing. I especially love how so many of the lines seem coded, though often unintentionally. The "husbands never dance with their wives." LaShawn's "ain't got a smidgen of rhythm between 'em" and her various putdowns of Randall's masculinity. The "why do women powder their noses just to go home and go to bed." If eye contact didn't send the message, reading between the lines sure would!