Traylor Howard (Natalie) really was pregnant during production. Thus, in every scene in which she appears, her stomach is concealed behind something, whether it be a car, a table, or a coat. The only exception is when Natalie "pretends" to be pregnant; then her stomach becomes completely visible.
When Monk assesses the laid out silverware on the table he finds a fork 'one centimeter too close'. When Mrs Murphy, head of housekeeping, says "it's only a centimeter" Monk corrects her with "For want of a nail the kingdom was lost" referring to the proverbial rhyme: For want of a nail the shoe was lost. For want of a shoe the horse was lost. For want of a horse the rider was lost. For want of a rider the message was lost. For want of a message the battle was lost. For want of a battle the kingdom was lost. And all for the want of a horseshoe nail.