Taxa in bold have extant representatives. Taxa for which monophyly is uncertain are followed by a question mark. Taxa whose phylogenetic position is less certain than presented here are preceded by a big orange question mark (this excludes those whose uncertainty is already indicated by a polytomy). In the lower right is a short list of taxa so problematic that we did not deign to place them in even a tentative position on the phylogeny (though we may have ideas about what major groups they belong to). This should not be by any means treated as an exhaustive list of controversies in vertebrate phylogenetics, as I have only indicated those we brought up in class.
All silhouettes are from PhyloPic, with the exception of the parvicursorine, which was generously made for me by when I lamented that I could not find any alvarezsaurid silhouettes on PhyloPic that were satisfactorily fluffy.
Due to the time and effort involved in creating an image of this size and nature, I am unlikely to update this on a regular basis. As such, this should be considered a snapshot of the state of the art and will inevitably become increasingly outdated as time goes on. However, a more up to date version including only the branching topology (but not the synapomorphy lists or silhouettes) is available here.
Thecodonty here is used in a stricter sense than simply having teeth set in sockets. Prolacerta, Proterosuchus, and many other non-eucrocopod crocopods exhibited ankylothecodonty, in which the teeth were not only set in sockets but also fused to the jaw, whereas plain thecodonty (as exhibited by Erythrosuchidae + Eucrocopoda) in this case refers to having teeth that are set in sockets but lack fusion with the jaw.
2. Bats sister to colugos within Archonta.
3. Pangolins sister to xenarthrans, with this clade close to Euarchontoglires.
4. Afrotheres close to laurasiatheres.
6. Procyonid pandas.
7. Suinan hippopotami.
8. Primate treeshrews.
9. Artiodactyls closest to carnivorans & perissodactyls closest to afrotheres.
10. Monophyly of noncetacean artiodactyls.
I also remember that orangutans, gorillas & chimps were once thought to form a clade exclusive of man. Is that dead in the water as well?