I recently finished interviewing some graduating High School Seniors (one-on-one) for their end-of-year banquet. They were given a list of questions, and were asked to write-down their responses, and practice...

During the interview, invariably someone would lose their train-of-thought, or otherwise mess-up.
No big deal, the answers were about 20 seconds each, we just did a second take.

During PP, I noticed that the second-take was ALWAYS better than the first.
It got me thinking for next year, should tell the Seniors up-front that we are going to ask/answer each question twice?
It would extend the interview time, but that is manageable.

The other option is to be more picky during the interview, and selectively ask them for a second take,
but I worry that after the 5th second take, I'm gonna start getting frazzled nerves

Don't tell them you're going for a 2nd take. I've worked with some top professional news readers doing offline interviews and news desk style reads for trade shows and in so many cases the 2nd is just better than the first read. Even if I knew I was going to do 2 reads, I never told them that.