Brian acts oblivious to how the toilet works but he has no problem flushing it in “Stewie Loves Lois”

The title “Bill and Peter's Bogus Journey” is a take off of the title of the 1991 Keanu Reeves & Alex Winter's sequel “Bill & Ted's Bogus Journey”

Peter: “Hey look kids it's a recreation of the lost city of New Orleans”

(Exaggerated) Reference to the flooding of 2005's Hurricane Katrina

Seamus: “I'll handle this, I've tangled with the likes of these before”

After Seamus throws the octopus against the wall, the manner in which it slides down the wall is a reference to the 80's toy “Wacky Wall Walkers”.
They were small, rubbery, sticky toys that came in cereal boxes.

Stewie: “He looks more pathetic than John Merrick when he went on Match.com”

Joseph Merrick, he was called John in the 1980 movie loosely based on his life, was known as The Elephant Man due to his severe case of neurofibromatosis type I, a genetic disorder also known as von Recklinghausen's disease.

Match.com (obviously) is an online dating service.

Peter: “...and the Pirates of the Caribbean wife”

Peter is referring to Maria Shriver

Bill Clinton: “You know where I got that nipple ring... ole' Straddlin' Madeleine Albright”

Madeleine Albright was the first woman to become United States Secretary of State. She was appointed by President Bill Clinton on December 5, 1996

Peter: “I don't know Reagan, I wish I could believe that”

Peter confuses Bill Clinton w/ the 40th President of the U.S. Ronald Reagan

Bill Clinton plays the instrumental theme on his saxophone to the sitcom Night Court that aired on NBC from 1984 to 1992

In order to teach Peter you're as young as you feel he takes him to Chuck E. Cheese where they play the video game Dance Dance Revolution.

Bill dances to and sings “Barbie Girl” by Aqua

Bill Clinton: “Uh hello, is this Linda Tripp? You shouldn't of talked you stupid bitch! I hope you die!”

Linda Tripp was a central figure in the Monica Lewinsky scandal of 1998 and 1999 that led to the impeachment and subsequent acquittal of U.S. President Bill Clinton

Farmer: “Now ladies and gentleman, Mr. Conway Twitty”

The live performance of Conway Twitty was taken from the country variety show Hee Haw that ran from 1969 to 1993.
The song he was performing is called “Your Love Had Taken Me That High”

He returns later in the episode as a distraction for Alexander Graham Bell performing the song “You've Never Been This Far Before”

Lois: “It looks like Muhammad Ali drew this”

Muhammad Ali suffers from Parkinson's Syndrome so a drawing by him would probably look like a one year old did it

This episode is the 2nd time Judd Hirsch has been referred to.
The first time was in “Blind Ambition” when apparently he is working in a missile silo underneath Quahog's bowling alley.

Bill Clinton: “You wanna give me that cigar, I'm ready to smoke it now”

During Clinton's impeachment trial, it was revealed that evidently a cigar was used in a way other than smoking. Lois may be using it in the same manner.

Lois: “I've been a worse wife than Lorena Bobbit when she was married to The Thing”

“The Thing” is a superhero from the Marvel world. He is part of the team “The Fantastic Four”.

In 1993, Lorena Bobbit because infamous for cutting off her husband's penis as he slept, driving away with it, and throwing it out the car window into a field.

Since “The Thing” is made entirely of orange rock, it was apparently pretty easy to find his severed penis

Uma Thurman on the set of 1994's Pulp Fiction

Carter: “Will you people quiet down, I'm trying to watch 'Medium'”

“Medium” is an NBC show that started in 2005 starring Patricia Arquette.
In May 2009, NBC announced the cancellation of “Medium”, however CBS immediately announced they would be picking it up for their 2009-2010 fall season.