When Brian and Stewie have tied up the family, the gifts put under the tree earlier are now gone.
When Santa's sled crashes in the front yard of the first house visited, the bag of presents splits open. Later it's seen that the bag is undamaged.
When Stewie and Brian drag the unconscious man into the closet, he leaves a thick trail of blood. When they close the door, the blood is no longer there.
Peter says "Oh and that reminds me 12 kegs of beer!" But he was sitting on 13 kegs.
When Brian and Stewie are trudging through the snowstorm, a bunch of snow can be seen collected on Brian's nose, up until they find the cabin and open the door. When Brian is closing the cabin door, suddenly his nose is clean.
When Brian tries to restart his Prius after the crash he inserts the ignition key and attempts to 'turn over' the engine. The Prius actually has a starter button not an ignition key. (The key simply needs to be inside the car to activate the button.)
When Brian and Stewie fly over the Statue of Liberty, the base is very different from reality, in that it's too small and is missing the immigrant inspection station among other things.
At the end when the camera zooms out, Cleveland's old house is nowhere to be seen.
In the last scene, the camera is above Quahog and pulls back so that the viewer can see a couple of hundred homes. Out of all of them, the only house decorated for Christmas is the Griffin's.
Cleveland is watching Quahog news even though he lives in Stoolbend, Virginia.
It makes no sense that Stewie and Brian are utterly overwhelmed with the workload of their Santa job, yet Stewie still found the time to convert the sled into a spaceship off camera.
Stewie claims there are two apartment buildings on the same block as the first house stop. However, in the aerial shot there are only more houses.
It makes no sense for Stewie to put yellowcake uranium on his Christmas list. The cheap and abundant mineral is of no use to anybody who does not own a gigantic enrichment plant.