A "medium" is another word for a psychic, so the title of the episode is referring to Peter as an "Extra Large" Medium.
Chris' back pimples ('bacne') spell 'citibank' in braille.
Stewie breaks the Fourth wall in discussing a poem by Henry David Thoreau pointing out the audience's perceived lack of knowledge when they believe most would attribute it to Thorton Mellon, a character in the film Back to School. Stewie himself made a mistake in "Fore Father" when he tells himself “do not go gentle into that good night.” which played a prominent role in the same movie. He first attributes the quote to singer-songwriter Bob Dylan but then corrects himself; it was written by poet Dylan Thomas. The name Thornton Melon from the film Back to School only has one L. It is spelled as "Mellon" with 2 L's when it appears on screen.
Stewie's Thoreau quote is a misquote. It's actually "I went to the woods...", not "I came to the woods..."
The British Guy presents his "fanny" to Chris, but in British slang fanny is a term for the female genitals. 
After Peter believes he is psychic, the sign at the front of the Griffins' house reads 'Psychic readings by Peter the mystical'.
A cutaway to the Enterprise from the original Star Trek shows Spock winning the lottery with 18, 24, 41 and 72, then swearing at everyone and leaving. Nana Visitor voices the Enterprise viewscreen in the cutaway. The part where Spock says "Live long and suck it" was claimed to have been created months earlier by the Nostalgia Critic.
Bristol Palin was heavily insulted by this episode because Ellen stated that her mother is the former governor of Alaska, which, she said, was clearly a swipe at her younger brother, Trig, who has down syndrome himself. Her mother, Sarah, was equally offended and discussed it with Bill O'Reilly on The O'Reilly Factor, calling the producers of Family Guy "cruel, cold-hearted people," while O'Reilly called Seth MacFarlane a "hater". In response, Andrea Fay Friedman, the real-life Down Syndrome girl, issued a statement that said Palin has no sense of humor. Seth discussed it with Bill Maher on Real Time.