Don says he named the chicken he has been carrying around in his backpack "Debbie." This is a nod to the original series in which Don found "Debbie the Bloop" (a chimp-like creature with a large cranium and extended ears) whom he gave to Penny as a pet.
The character of Angela is an homage to Angela Cartwright, the actress who played Penny in the original series.
When the parents and Don west arrived at the crash site of the Resolute piece, both doors on the pod opens up, the view from above the pod makes the pod looks like the original series pod, which had a big rectangular window.