Many classification theorems (e.g. of the finite subgroups of $SO(3)$, or the finite-dimensional complex simple Lie algebras, or the finite simple groups) have some infinite lists, plus some "sporadic" or "exceptional" examples.
It was opined in http://mathoverflow.net/questions/112715/why-when-classification-of-simple-objects-is-simple-e-g-unknown-classifica that any such theorem only reflects our current knowledge of the subject. One might hope that better understanding would lead to an alternate way of slicing up the set of examples, with fewer sporadic cases.
Are there actually examples of this happening? I want a case where the initial classification is actually complete and correct; it's only our human description that has improved.
Two non-examples: (1) As I understand it, Suzuki found an infinite family of finite simple groups, that we now regard as twisted Chevalley groups for $G_2$ and its outer automorphism in characteristic 3. But that was before the classification was complete. (2) Killing had two root systems that turn out to both be $F_4$. So he wasn't quite correct.