The song Peter sings in the bar ("My Dear Old Irish Dad") is a parody of the Irish folk song "Dear Old Donegal".
O'Brian the sheep parodies Brian the dog's famous line "whose leg do you have to hump to get a dry martini?" substituting "a pint of Guinness" for the martini.
When Peter says, "I wonder what else I repressed", then smacks himself on the forehead, and says "Oh my God, I could've had a V8!" is a reference to commercials for V8 vegetable drink, in which actors smack their foreheads while making that statement.
The name of Peter's biological father, Mickey McFinnegan, could be a reference to "Mickey Finn," a once-popular slang term for drugging someone's drink (as in "slipped him a Mickey").
When Peter and Brian arrive in McSwiggin Village, they're seen exiting a black Hackney cab. These cabs aren't used for commercial purposes outside the UK, and regular cars are used for taxiing in the Republic of Ireland.