Did the list not have the age of each voter printed on the list. In Texas they do. Even without a photo ID, it an election judge should be able to determine that a college age adult isn't a 70 year old.
Probably not. I live in Massachusetts, about five minutes away from the New Hampshire border, and we pretty much do it the same way. The only thing on the list is your name and address. In fact, I still see my sister's name on the books when I go to vote, even though she moved out of state over ten years ago.