There was a considerable body of evidence against the WMD story right from the start. Senior CIA personnel were crying foul at how their intelligence was being manipulated for political ends from an early stage, it's just that evidence wasn't enough to stop the war.
Nothing remotely like that ever happened with the Apollo program. There has never been any substantial evidence or testimony against it from within government or NASA, or as Neil pointed out from any foreign specialists or experts, even the Russians. Conversely the WMD story was being challenged internationally from it's conception, as you pointed out yourself.
In terms of challenges, counter evidence and controversy at the time the two cases could not possibly be more starkly utterly different, and that's why they are useful comparisons because the WMD thing shows clearly how government deceptions actually work out.
Maybe we have a different understanding of "failed" or "immediately", but it worked well enough to get the media on board to build a case for war and carry it for long enough until the actual war started. It was solid enough that even all the doubt coming from NATO partners (and the flat out refusal to be part of it with Chirac's utterance that "France is not a pacifist country" and it's not about war itself but that war and those reasons in particular that they wouldn't be a part of it) did not stop the war. So, to me at least, it didn't fail at all, it succeeded.