Kks74 has はっきり explained it already, but I typed this before noticing I hadn't refreshed the page, so I'll post it anyway.
間違いない is more like "not wrong, not mistaken". It's more to do with correctness and probability -- saying you are certain that you are not wrong. 間違い "error, mistake" (noun) from the verb 間違う "to be incorrect, to be mistaken".
はっきり means "clearly", "distinctly". This is more to do with there being no ambiguity, no vagueness, not messy, easy to interpret, plainly evident, crystal clear. I don't think this is the origin of the word, but think of 晴れ (はれ) "clear weather" + ～きり adverbial word ending.
However, for that question you encountered, I agree that either word could be used in situations giving that kind of meaning. Unlucky.
I think はっきり has a very strong meaning of "clearly" though, so I would be very cautious about clicking that answer if "clear" wasn't listed somewhere in the question, but this might just be how I think from using JCJP for so long. And as you said, はっきり is an adverb, so "certain" rather than "certainly" might be another hint that this might not be the answer it's expecting. ^^
July 3, 2015 at 9:18pm
what's the differerence between 間違いない and はっきり ? adj and adv respectively ? or else ?
Well I don't know a lot about this kind of situation in Japanese but in English you use clearly this way "The mountain was clearly visible" but without doubt as "He was without doubt about his plan". I suspect there may be a similar situation in Japanese but I can only guess. I notice 間違いない has "nai" so it is definitely "doubt none of" but はっきり is just "clearly". Not sure if that helped because I am a confusing person in general but perhaps someone else can elaborate on this.
Kks74 has はっきり explained it already, but I typed this before noticing I hadn't refreshed the page, so I'll post it anyway.