Sorry, but I saw no signs of anyone squirming. Trump did not seem terribly comfortable, though.
Of course, no one mentioned that the Certificate of Live Birth that has been posted over and over is adequate to get a passport or a drivers license anywhere in the US, and should therefore be entirely adequate to run for president.
The only thing that could possibly be embarrassing that I can think of is that his mother was listed as "unmarried" or the blank where his father's name would be written indicated "father unknown".
Neither of which should have any relevance about his eligibility.