Should I check puncture-resistant tires for glass etc.?
Even if the glass doesn't work through the puncture proof layer (which it will, eventually), it's still a good idea to check once in a while for cuts etc, especially in the side walls, which almost never have a puncture proof layer. It's a "better safe than sorry" approach, but it takes all of five minutes to check both tires, so in my opinion that's time well spent if you know what happens when the tires blow out on a descent or, in your case, running a green light very late.