Why is Continuity Important?

Continuity is important because it maintains the realism of a film or TV show, making any scene that was filmed multiple times seem as though it was shot in one take. It's not just seen in terms of makeup but also any props on the set, for example; a candle burning at a specific height or a lamp in a specific place on a shelf. On the set, one specific person is in charge of making sure that the continuity is maintained throughout the shoot - The Script Supervisor. 

In order to maintain the continuity throughout, extensive notes are made about each element with pictures also being used to help add to the notes. These pictures are taken from numerous angles to get as much detail as possible, and are taken at the end of each setup or at the end of the day.
Lack of continuity can be carefully planned so that it does add to the effect of the film, by doing so it can create confusion for the audience thus distorting the image and making it seem obscene as a result. However this shouldn't be overdone as it does lose the effect, which would make the film look incredibly amateurish and jarred in the final product.