The story had a supply of insulin being mailed to Christine's apartment, and other vials of insulin being found in Dr. Solway's desk. Insulin breaks down at room temperature and must be kept refrigerated or kept cool with cold-packs while in transit: the mailing package shown was too small to contain both a vial of insulin and a cold-pack, and the unrefrigerated insulin left in Dr. Solway's desk would have become useless very quickly.
Olivia talks about a web site she has seen that gives teenager girls advice on how to become "anorectic". An anorectic is a drug that suppresses appetite. Olivia presumably meant to say "anorexic", referring to the eating disorder.
Dr. Solwey says she's been deaf since birth, but if that were true she wouldn't know how speak or to form words with her mouth as she signs.