Not understanding prevalence and pre-selection in statistics. That sounds very technical, but it goes down to a lot of misunderstandings: e.g. if you take some medicine and you are healthy again after 7 days, but the disease would normally disappear within a week anyways, then this is not a proper medicine.

Or if someone says that doctors, musical conductors, etc. "live longer" than then average person, then they forget that you need to already have lived to a certain age to make it to this kind of profession, i.e. you can not die as a teenager any more, so the average is shifted.

Or if people assume that palaeolithic people lived in caves: surely they must have used caves where they were available, but just as sure they already had simple housings, tents, etc. It's just that only in the caves we have found their remains, whereas the others have just withered away.

And, and, and... there's so much of it...