Suppose I washed two dishes. When my mom checked them, she said, "This one is OK, but the other one is no good."
Is NO GOOD used correctly here?
One wouldn't normally worry about a parent's adherence to abstract rules of grammar in situations like this - if you could find any that were relevant. It's fine.
I think 'Not good' probably started life as a hypercorrect form of 'No good' - perhaps among Spanish speakers (underlining the equivalence 'not (Eng)=no (Sp)'). But 'not good' was always possible in some contexts - where it meant 'the opposite of good' rather than just 'bad' - and is now acceptable in many more.)
b
Chanbr, I think you're looking for this: no good - Idioms - by the Free Dictionary, Thesaurus and Encyclopedia.
"Let's see if this soup is any good."
Tastes soup.
"Nah, it's no good."