My policy...
When I start to hem and haw and flipping a coin deciding about the condition of a tire, I just pull it off. It's worth peace of mind. New tires might be more prone to picking up pieces of debris/glass, as the rubber is sticky, but that depends on the brand of tire. I use Shoe Goo to patch up small nicks and cuts, but if I go around my tire and see a whole bunch of patched spots, I replace the tire, but these are usually tires that are at the end of their tread life. I used to make a habit to brush my tires with my gloved hand while riding, but I found it did not make much difference. I do brush if I think I ran over something. I started riding with amber or clear lenses, unless the sun is very bright. Riding solo your more apt to spot what you are riding over, riding in groups you are more focused on other things. I'm very fussy on tires as my "big crash", which laid me up in the hospital for a week, was caused by a blow out with my front tire. I just pay more attention to what is in front of me now and take a look at my front tire before I start a descent. They just cleaned the roads I ride on, which is a twice a year occasion (if that), so all the old glass has been removed, now I just have to watch for the new stuff. But I'm fairly lucky as most of my roads are glass free, I just have to watch out for gravel and small rocks.
Tires are always a pain, but don't let the pain be the type that keeps you off your bike. When in doubt, chuck it.....