There were only two things that bothered me, and they were completely out of control of the contest itself: one was the kind of icky, condescending and almost racist illegal-aliens running gag (and why didn't that turn into a gag about actual aliens, anyway?)

I think because it was intended to be a comment on current affairs. I didn't perceive it as racist.

I think the "euphemism" running gag developed because it was funny, not because anybody was afraid of shocking the kids or their parents.

I agree. If only the contestants' timing had matched the panelists and generated a match -- but OTOH, the fact that they were out of synch may have made it even funnier.