Bob Cratchit and Tiny Tim go to a butcher's on Christmas Eve to pick up a duck. In the original novella, which this purports to be intersecting with, the Cratchits had goose for Christmas dinner, not duck.
The three Ghosts of Christmas are seen arriving at Scrooge's home together, immediately after Marley's ghost departs. If the story of A Christmas Carol is meant to be a true retelling of these events, as the episode asserts, the spirits arrive separately, hours later, and the Ghost of Christmas Yet to Come did not meet Scrooge in his home, but out in the city where the Ghost of Christmas Present had abandoned him.
Upon retrieving them from the containment unit, Egon has the three Ghosts of Christmas enter the trap, reasoning that it will be faster to transport them to Scrooge's that way. The Ghosts have been shown to possess supernatural abilities, including flight and instantaneous teleportation. Putting them in the trap and running them to Scrooge's would take vastly more time than allowing them to travel their on their own power.
The characters repeatedly refer to the famous Ghosts of Christmas from their recollections of A Christmas Carol as the Ghosts of Past, Present, and Future. The ghost of the future was called the Ghost of Christmas Yet-To-Come in the novella.