The importance of continuity

The script supervisor has the responsibility of making sure that continuity is maintained between takes and scenes or setups. Continuity is vital for creating enjoyable, believable stories in films: if characters' appearances, props, or scene setup changes between shots, the viewer is reminded that what they are watching is not a depiction of real-life; instead, it becomes just a series of video clips that don't quite fit together. Everything has to look exactly the same - the exact placement of wounds, where clothing or hair sits on a person, where props are placed, lighting, camera angles, and so on. To do this, careful notes need to be made and followed, and numerous pictures are taken throughout filming. 
Each individual department of a film crew will take front, back and side images, close-ups and full body shots, and make many detailed notes. All notes will be dated with the scene number and the day of the film sequence. 
A common problem is when filming pick-up shots later on in the production of a film. The original costume and make-up artists may have moved on to another project by then, so another team is needed to recreate the same effects as before for shots that need to be inserted. If a lot of time has passed between filming, actors' skin, hair or physique could have changed colour or length or shape; it is important, while watching the film back, that continuity notes are made, so that when filming further shots the actor can be made to look the same. Costumes or wigs may need to be re-hired from companies. Otherwise, when all the shots are edited together, the characters will keep changing appearance back and forth, which will ruin the viewing experience. 

http://www.delamaracademy.co.uk/blog/2009/06/an-introduction-to-continuity-for-the-make-up-artist