When Steve Claus enters Gwen's house, he steps on a small toy sheep which makes a distinct "Baaa" sound. This is a "Shaun the Sheep" toy. Shaun the Sheep (2007) is TV show produced by Aardman Productions, the same company behind Arthur Christmas.
Script writer Peter Baynham, born in Cardiff, Wales, included a reference to an obscure bit of Welsh history in his script, with Mimosa Avenue in Trelew. In 1865, about 150 Welsh emigrants sailed on the ship Mimosa to Patagonia, Argentina. They founded a town called Trelew, where there is now a street called Mimosa, after the ship. Baynham postulated an avenue by that name in Trelew, Cornwall, to complete the confusion between the two locations. (The movie's placement of Trelew in Mexico, instead of Argentina, is apparently an error.)
In the delivery scene in the beginning of the film, one of the elves puts down a wrapped rail road track in front of him as he is riding on the train. This is in reference to the scene in The Wrong Trousers, another Arrdman production, where Gromit does the same thing in the Penguin chase.
As the last gift has been delivered and mission control is celebrating, a solitary elf with a crew cut is seen wiping a tear of joy from his eye. This seems to be a homage to the scene from Apollo 13 when Ed Harris (playing Gene Kranz, Flight Commander) has a silent moment of joy when NASA safely return the crew back to earth.
During the short scene when they are watching the news describing a fast moving UFO, there is a voice that sounds like Tom Hanks describing the UFO as a steam train. Possibly referencing The Polar Express (2004).
The S-1 flew over Trelew, Mexico twice; Firstly, of course, to deliver all the necessary gifts to the residents and children that live there and secondly because of Santa's poor navigation skills, attempting to get the superior present to Gwen, when he, like Arthur, keyed the address, saw a list of 'Trelew's and selected the first one, resulting in Steve descending on the '23 Mimosa Avenue, Trelew, Mexico' address (where Pedro lived, and where Arthur and Bryony mistakenly went into, only to discover a bike-like gift wrapped under the tree there). On the other hand, The S-1 also flew over Trelew, England. Firstly to deliver the necessary gifts to all the other houses in Gwen's hometown and the second time to deliver Gwen's missed present.
The trivia item below may give away important plot points.
When Grandsanta, Arthur and Bryony leave Tanzania to set off for Trelew, Arthur programs in '23 Mimosa Avenue, Trelew' into the Ho Ho. After they break into the wrong '23 Mimosa Avenue' in Mexico, Arthur stated that "the Ho Ho came up with a list of Trelew's and he clicked on the first one", which was Trelew in Mexico. Later on in the film, we learn that Santa did the very same thing, which is how he ended up giving the superior present to the Mexican boy, Pedro, who lived in 23 Mimosa Avenue, Trelew, Mexico. This is the same address that Arthur & Bryony broke into.