Yes, CONTINUITY is a Scrabble word!

Letter values in Scrabble US: C 3, O 1, N 1, T 1, I 1, N 1, U 1, I 1, T 1, Y 4.

Is it a valid word?

CONTINUITY is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

uninterrupted connection or union
a detailed script used in making a film in order to avoid discontinuities from shot to shot
the property of a continuous and connected period of time