When Alaska walks towards Miles she has nothing behind her ear but when she sits down she has a cigarette behind it but you never see her put it there.
At the beginning of the episode, it is clearly stated that the show is set in 2005. However, during the drive to Culver Creek Academy, the Halter's car is seen passing through a highway intersection among cars (including a 2018 Nissan Murano) that are clearly from a much later time period.