One interesting group that survived the K-T event only to die off in the Tertiary (latest survivors in the Miocene) were the crocodile-like champosaurs, a group within the Choristodera.
One member, Lazarussuchus, was so named because it represents a “ghost lineage,” a late appearance of a form (in the Oligocene and Miocene) of a group that had apparently been absent from the fossil record for many millions of years.
Excuse me for nitpicking this a little, but there are actually six species of tree sloths in two genera, the Two-toed Sloths Choloepus and the Three-toed Sloths Bradypus. Oddly, the two kinds of tree sloths are not very closely related, being independently evolved from two different families of ground sloths.
I know the 2-toed are Megalonychids (otherwise ground sloths) – but I thought the 3-toed were their own family, the Bradypodidae.
I think the OP is less about dinosaurs and more about epistemology. He’s asking how closely we can come to certainty, with incomplete evidence.
The ground sloths include five families, the Megalonychidae, Megatheriidae, Mylodontidae, Nothrotheriidae, and Orophodonitidae. As you say, the Two-toed sloths belong to the Megalonychidae. The Bradypodidae, including the extant Three-toed Sloths, seems to be more closely allied to the Megatheriidae - the really enormous ground sloths including Megatherium and Eremotherium - than they are to the Megalonychidae.
No worries.
Thanks. 
That helps clarify things for me, at least.
Agreed. What we know, we know from the fossil record, and it is necessarily incomplete. Soft-bodied forms in particular are very difficult to trace lineages of, since they only get preserved in a few Lagerstatten. For example, there is either a remarkable bit of convergence on a highly unusual body form, or there were soft-bodied forms throughout most of the Paleozoic with great appendages. Opabinia and Tullimonstrum are clearly closely related – but save for a handful of Lagerstatten, mostly Cambrian except for the Mazon Creek formation from the Carboniferous (source of Tullimonstrum), those forms were not preserved.
While dinosaurs had hard parts, they were land animals, and were preserved only where their corpses landed in sediments that were preserved. Animals that lived in forests or upland areas might not be well preserved.
But all that said, the fact remains that dinosaurs were universally present prior to the K-T and completely absent from the fossil record (redeposition to one side) thereafter. That says something important, even if it doesn’t prove extinction to the satisfaction of a total linguistic pedant.
What about the tuatara?
Not even close.
Birds are dinosaurs – the one group of small sauriscihians that evolved feathers and flight, and survived the K-T event.
Crocodilians are archosaurs – depending on your classification scheme, they might be as closely related to tyrannosaurs as triceratops is.
Tuatara are more closely related to lizards than to crocodiles Not dinosaurs, but not crocodilians, either. If that’s what you meant.
Slow Foot? I don’t know why but that amuses me greatly.
Though it’s amusing to note that T. rex is more closely related to sparrows than it is to triceratops. This, incidentally, is the reason that birds are considered a subset of dinosaurs.
Sorry – you’re entirely correct, and I confused things by how I said what I said.
Lizards, snakes, and tuataras are lepidosaurs, one large group of Eureptiles.
Dinosaurs, including birds, pterosaurs, and crocodiles are archosaurs, andother large group.
My statement was intended to be “tuataras are not even close to being the closest surviving relative of dinosaurs; crocodilians are the non-dinosaurian survivors that are closest” or something of that sort.
I think that means “Man-who-was-living-with-three-boys-of-his-own Foot”
And Choloepus means “lame foot.”
And is probably the only living mammal which belongs to a family whose type specimen was described by a U.S. President.
So birds are dinosaurs, but assorted Jurassic-era saurian reptiles weren’t. Am I saying that right?
I thought that was oedipus.