During the song 'We Got The Beat' when Rachel, Santana and Brittany stand on the tables, their order repeatedly changes between shots.
When Kurt and Rachel are talking in the car it is raining on Rachel's side of the car. The camera then cuts to Kurt and the first two times his side of the car is completely dry until the third cut to him.
While Kurt may not have been familiar with NYADA, it seems very unlikely that Rachel and her dads would not have known about NYADA and also the fact that Juilliard doesn't have a musical theater program. (Juilliard does, though, have an acting program that features vocal training for the last three years, as well as dance and movement training.)
Santana tells Quinn that they could win 2 national championships. They should already have 2 being seniors, freshman and sophomore years, since the show starts out their sophomore year and at that point Sue took her 5th consecutive national championship.