The quote "No man is an island" which Will jokingly attributes to Jon Bon Jovi, was actually written by John Donne in 1624, in his work "Meditation XVII".
When Will is hit with an apple whilst singing on stage with Marcus, the apple was actually a sponge ball purchased from a local sports shop, painted to look like an apple.
The shot of Will reflected in the mirror when he is depressed was actually taken when Hugh Grant was taking a break. The directors noticed him doing this and from behind he looked depressed, so they shot it without him knowing.
After the Christmas dinner scene we see a clip of Marcus in school followed by the New Year's Eve scene with Will and Rachel. There is no school between Christmas and New Year's in the UK.