"Doesn't it taste good?"
Im pretty sure Duolingo is right about this one - but they don't offer grammar explanations so if you have limited outside experience you won't be getting the subtle difference.
In sentences such as this one; using a negative adjective (adj + ない ending), and ending with a question か plus rising intonation in spoken language, requests agreement (i.e. "isn't it", "doesn't it", etc).
Versus asking if something is not alright I feel would be along the lines of an 〜ありませんですか ending.
I could always be wrong, but I'm pretty sure to ask if something is not tasty versus asking for agreement would be "おいしいではありませんですか"
I agree with osoikoibito. The following 2 sentences have different meanings: Doesn't it taste good? Does it not taste good?
This is where duolingo confuses me. I have always thought that the negative form of adjectives in Jap translate to NOT+adjective. Because in class we have sometimes used the negative adjective form interchangeably with the antonym e.g. not expensive = cheap; yes it's not completely the same but it depends on the context.