When the family is mediating with Cleveland on whether or not to get back with Loretta, Peter accuses Brian of pushing Cleveland back with Loretta just so he himself could have Carolyn, and Peter says, "You know, Brian, sometimes I don't believe I know you", in a low and harsh tone; this is a quote from The Sound of Music, where Captain Von Trapp utters the same thing to Max Detweiler in response to his indifference to the Nazi invasion of Austria.
When Lois asks Brian if he really thinks Loretta is beautiful, Brian replies "Absolutely!" and then goes into a lie-filled speech which is almost the same speech that Dr. Rumack gives to the passengers in the movie, and his nose grows longer and longer just as Rumack's nose did.