Oh, please! Transgender is kind of a funny word, and it sounds a bit like an airline. Still not a very good joke, but...
I think Colbert ignored it because the moment he heard the word "transgender" he assumed whatever was said would be taken as transphobic. By cis people. Personally I'm more concerned with people being idiotic hateful pigs than with them being politically incorrect.
And about that first joke, I played it several times and I still can't catch what Colbert said just before, but it was something about his son.
What bothered me the most about the video was the ostentation, that's probably my Swedish upbringing.