23. Solution: (1) When $a = 1$, $f ( x ) = | x - 1 | x + | x - 2 | ( x - 1 )$ .
When $x < 1$, $f ( x ) = - 2 ( x - 1 ) ^ { 2 } < 0$ ; when $x \geq 1$, $f ( x ) \geq 0$ .
Therefore, the solution set of the inequality $f ( x ) < 0$ is $( - \infty , 1 )$ .\\
(2) Since $f ( a ) = 0$, we have $a \geq 1$ .
When $a \geq 1 , x \in ( - \infty , 1 )$, $f ( x ) = ( a - x ) x + ( 2 - x ) ( x - a ) = 2 ( a - x ) ( x - 1 ) < 0$ .
Therefore, the range of values for $a$ is $[ 1 , + \infty )$ .