When Catherine checks the texts on her phone, the battery is at 45%. Hours later, after continuously working the case, and not recharging the phone, she checks the texts again and the phone is now at 62%.
Joshua says that the DNA from a killer's tooth shares an allele (a variant of a gene) with the new-born infant and concludes that the killer is female and the mother of the infant. This is nonsense. One single allele could be shared by millions of people. Identifying someone (or family relationships) requires the two DNA samples to have many alleles in common. Also, a single allele could not determine biological sex.
When Lindsey texts Catherine at the end of the episode, her text appears blue. Incoming texts on iPhones are gray. OUTGOING texts are blue (if the other person has an iPhone).