Yeah they do, and a lot get caught. But errors, even ones like this, slip through the cracks all the time. It's certainly not unusual.
How could this one have gotten into circulation, if not in a roll? I don't really by what other means cents are distributed in the US. How did it make it into a collection and into a slab?
Well for one thing the mint doesn't put coins into rolls. The mint ONLY distributes coins in bags. Only private companies put coins into rolls. But they (private companies) don't put all coins into rolls, some are sent out in bags as well, but smaller ones than what the mint uses.
I, too, have a birthday in this month of February, I will be 21 again for the umpteenth time. My first 21st birthday was the birthday anniversary where I stopped counting. I'm glad to see so many people with young children getting them involved in collecting coins. These young numismatists are the future of the hobby.