In my opinion, "that's not good" means the same as "that's bad."
For example, if Joe is bringing all the food to a party and he calls and says something came up and he can't come to the party after all, I would say, "oh dear, that's not good!"
"That's no good" means something more like "that won't work."
For example, if Joe says he'll bring all the food to the party, then shows up with only plates and says "I couldn't bring food so I brought plates instead," I would say, "well, that's no good!"
That being said, in many circumstances, they can be interchangeable. However, the subtle implication in each case is different.