The Stupidest Claim of Yec'ism is....
Well, the simple answer is their claim that the earth is young. Yes, it's a bit boring I know, but it really is the stupidest claim that young earth creationists make. The scientific evidence favoring an earth older than 6000 years is overwhelming and makes any counterclaim appear exceedingly silly. The only real reason for having a young earth is so that evolution does not have time to take place and that means humans are somehow special. In fact, the only evidence for a young earth is a literal reading of Genesis and the assumption that the post-Adamite generations are a true history of all humankind. There is no independent corroborating evidence to support this claim. Just about ll the idiocies mentioned in previous posts flow directly from the assertion that the earth is young.
I think it's also interesting that, despite howling protests from the Intelligent Design camp, the goal is the same as young earth creationists. All their pleading about bacterial flagella are not really about elevating bacteria to a special place, but about using the same illogical arguments to support the claim that humakind could only have gotten here via special creation. ID'ers try to distance themselves from questions regarding the age of the earth because it is politically expedient to avoid discussing that issue. What is truly amazing about ID-creationism is that in attempting to get theocracy established via a back door, they are forced to abandon their belief in the very document that fueled their efforts (and yes, I know they've co-opted a few token non-Christians into the effort).