The watchdog has confirmed that some viewers voiced their disapproval, although the number of complaints and their details have not yet been stated.
Jack Whitehall, James Corden and other comics made jokes about the Queen, President Obama and Susan Boyle during the show.
Whitehall notably made a joke about why the Queen had remained standing throughout her Diamond Jubilee celebrations, linking it to Prince Philip being hospitalised with a bladder infection.
"I'm just saying what everyone's thinking," he said.
The comedians also joked about the Twitter mistake made by Susan Boyle's PR team earlier this year, when they invited fans to join #susanalbumparty.
Other guests on the quiz show's panel included TV presenter Jonathan Ross, IT Crowd star Richard Ayoade, comedian Russell Howard and sports presenter Gabby Logan. The show was presented by Jimmy Carr.
Whitehall admitted on Twitter that he and teammate Corden had been "so, so drunk" when they filmed the show.
A Channel 4 spokesperson commented: "Big Fat Quiz Of The Year is a well-established comedic and satirical review of the year's events with well-known guests and is broadcast after the watershed with appropriate warnings."