Peter's sudden reaction at the end of his long speech with Quagmire is a homage to Jackie Gleason.
The gag of the unfinished drawing of the traffic jam is an homage to the cartoon Duck Amuck.
The gag involving the grandfather reading the storybook to his bed-ridden grandchild is a reference to The Princess Bride in which a very similar story interruption occurs. The character is intended to be Peter Falk who performed the role in the film.
When Quagmire asks Meg to come in his house for some Crystal Light, she says "Well, I do believe in me." This is a reference to a 1980's Crystal Light marketing campaign that used the slogan "I believe in Crystal Light, because I believe in me."