Ken Natton said:
The last common ancestor of humans and elephants is the last common ancestor of all mammals. An astonishing amount is known about this species – it most closely resembles a modern rodent.
This can not be true. Both humans and elephants are placental mammals (i.e., eutharia). Neither monotremes nor marsupials are descended from the last common ancestors of all placental mammals. Thus, the platypus and the kangaroo could not be descended from this common ancestor of humans and elephants.
As far as looking like a rodent: It depends on which rodent.
To get a better idea of what this common ancestor looked like, I reviewed:
"The Ancestors Tale" by Richard Dawkins (Mariner Books, 2004).
Dawkins claims that the Afrotheria were the "last placental mammals to join are pilgrimage". This means that the common ancestor of the Afrotheria is the ancestor of all the placental mammals. The Afrotheria lineage includes both elephants and human beings.
The Afrotheria split off from the other placental mammals about 105 million years ago. The rodents split off from nonAfrothere mammals about 75 million years ago (page 179). The rodent lineage does not contain elephants. Therefore, rodents are closer related to us than elephants. Rodents don't look anything like elephants, manatees or other Afrotheria. Therefore, I don't think that one could comfortably say that the common ancestor of elephants and humans resembled rodents more than elephants.
If one has to make an analogy between the common ancestor of all placental mammals and an extant mammal, then let it be the elephant shrew. The elephant shrew superficially looks like a rodent, anyway. It happens to have a long nose like an elephant, but it has generalized teeth roughly like a rodent.
No one knows yet whether the long nose of the elephant shrew is homologous to the trunk of the elephant. However, no one has proven that the long nose is merely analogous to the trunk of an elephant. The generalized teeth resemble (vaguely) those of a human more than those of an elephant.
Now, one doesn't have to insist that a common ancestor "look like" any extant species. However, making such comparisons helps wrap ones mind around the concept of evolution. Therefore, I propose the following. The common ancestor of elephants and humans looked vaguely like an elephant shrew.
Cute little fellas, too!