A group of street carolers sings "Joy to the World" in the film. However, the movie takes place in 1843. The song "Joy to the World," as we know it, wasn't created until 1848, when Lowell Mason, a Boston music publisher, combined two separate works from the mid 1700s: music from George Frideric Handel's "Messiah" with lyrics from another hymn by Isaac Watts. Also, "Joy to the World" was originally used as a regular Sunday hymn. It wasn't considered a Christmas song until 1911, when a recording by singer Elise Stevenson and the Trinity Choir became a Christmas hit.
Scenes showing London from the air incorporate numerous anachronistic features, including the Millennium Footbridge (opened 2000), the reconstructed Globe Theatre (opened 1997) and Southwark Bridge (opened 1921).
In the scene where the Ghost of Christmas Present shows Scrooge the two children, the boy says "Naff off!" to Scrooge. The expression was not coined until the 1960s and did not enter general use until the following decade when it was used as a substitute for swearing in the popular, early evening BBC comedy, Porridge.
When the first spirit visits Scrooge, servants' bells are shown mysteriously jingling in his bedroom. Bells tell the servants which room of the mansion is calling for them, and weren't normally placed in the master's bedroom. They were usually installed in the kitchen, the pantry, or the servants' chambers. However, Charles Dickens explained that Scrooge's large house had been subdivided and let out as office space except for a "suite of rooms" that Scrooge kept to himself as living quarters. Dickens states that there was but one single disused bell in Scrooge's chambers - which "communicated for a forgotten purpose" with another chamber higher in the building. Dickens notes other bells in the house also began to ring. Disney chose to put all the bells in the room with Scrooge, which is inaccurate according to the Dickens work and contrary to the way servants' bells were normally placed.
Some of the carolers seen at the start of the film appear again towards the end of the film singing 'Joy to the World' but given this scene takes place 7 years later the carolers seen at the start of the film have not aged one bit.
Marley tells Scrooge that one spirit will visit him at 1:00 am for the next three nights, but they all appear to him in the same night. This is repeated verbatim from the book, in which, following all the visits, Scrooge calls them "clever spirits" for doing it all in one night.
According to Scrooge's 'future' tombstone it says he was born in 1786 meaning Scrooge is just 2 months short of his 58th birthday but he looks more like he is in his seventies from his appearance to a use of a walking stick.
Correction - The reason Scrooge looks all old and haggard is to show that he's aged prematurely due to his vile attitude towards the world.
When Scrooge re-visits his old classroom; the ink markings and spill patterns are virtually identical on all the desks. The animators more than likely just placed several copies of an original desk throughout the scene.