Wow, lots of great responses to Monday's challenge! Some of you came very close to the particular aspect of the anatomy I was thinking of, though nobody got the specifics. However, many of you brought up additional issues with the reconstruction so I'll address some of those observations below before I get to the real answer.
1. Trish brought up the Coot-like lobed feet. While not the major fix I had in mind, this is also something I had already changed in the new version. The toes of Hesperornis are extremely similar to Grebes in terms of their anatomy, so while no soft tissue impressions of the toes exist for this group, it is almost certain that the toes were lobed rather than webbed (as in Loons and many other diving birds). I had initially based my illustration on this model, which restores the toe lobes divided into somewhat Coot-like segments. However, given the similarity to Grebes, it's probably a safer bet to go with a Grebe-like foot, with non-segmented, asymmetrical lobes (that is, like the flight feathers of birds, the 'vane' of each lobe would be small on the outside edge of the toe but broad on the inside edge). As this was still a work in progress when I began the revisions, I didn't yet add to the podotheca (foot skin covering) with its distinct scutes, but skin impressions from Parahesperornis show that they were present and, again, fairly Grebe-like in appearance.
Above: The feet of Hesperornis probably looked very similar to those of this Grebe.
2. Nobu Tamura pointed out that I bungled my interpretation of the leg integument. Good catch! In my own defense the text of Williston 1896 (which described skin and feather impressions in a specimen now referred to Parahesperornis) isn't exactly clear on the issue and the figure doesn't help much. Williston wrote: "I count twenty-six [metatarsal scutes] on the slab, and to the back part of the bone, while impressions of the feathers will be seen on the opposite side. These feathers were evidently long, reaching nearly to the phalangeal articulation". I remembered this as saying that the feathers essentially cover the tarsometatarsus and that the scutes were present close to the phalanges, but re-reading it sounds more like the MTs were only partially covered in long feathers (on the proximal part of the bone?) while the scutes were present across the distal part. The feathers were long enough to reach the toes, forming some very odd 'bellbottoms' around the scaly part of the metatarsus. I've tried to make this more clear in the new version.
3. Several people suggested that the wings are too prominent/visible, and honestly I'm not sure about this one. I don't know of any research on forelimb musculature that could suggest whether they were external or internal to the body wall, or whether or not they'd be useful in steering or something. I suppose we artists have license to go either way on this one right now, but as you can see I've de-emphasized them in the new version. The old one began to strike me as too Penguin-like, suggesting (even subconsciously) a role in propulsion that was probably not there in life.
4. Marco Tedesco wondered if the orange feathers on the head were incorrect. I have previously blogged about the likelihood of certain feather colors based on diet and structure. However, I don't think Hesperornis would have had much trouble sinking its teeth into some carotenoids to deepen the chestnut hue possible through melanin alone into a richer orange. We know that many cephalopods (including, apparently, some ammonites with preserved pigment) contain deep red carotenoid pigmentation, as do many fish, both of which may have been parts of hesperornithine diet. And in fact, these are colors found in modern Penguins. While on the subject of color, I chose to give Hesperornis a distinct, Penguin-like counter-shaded pattern. It seems to me that counter-shading gets apparently stronger in several independent lineages of diving birds, with more specialized diving forms (Penguins, Loons, Auks) wearing similar black/white colors (at least among breeding males) while less specialized forms (ducks, etc.) are counter-shaded with more subtle earth tones. Hesperornithines are probably the most specialized diving birds of all time (Zinoviev 2010) so it made sense to me to give them generally Penguin or Auk-like coloration.
Ok, now on to the "real" answer. Several people got this pretty close. It does indeed involve the hindlimb anatomy, including the position of the femur, the degree of sprawl in the legs and, ultimately, the life posture and ability to move around on land.
Several online sources have stated that Hesperornis was unable to walk, and must have instead slid around on its belly when on land. As I hinted in the last post, the Web site for the BBC show Sea Monsters (and possibly the show itself which I haven't seen) flat out states that they couldn't walk. But as we all know, TV documentaries are not exactly reliable sources. I tried and (initially) failed to find any support for this in the literature, aside from Marsh's own speculation in his famous Odontornithes monograph: "It may be fairly questioned whether it could even be said to walk on land, although some movement on shore was of course a necessity."
Two pieces of information can be combined to give the answer, the second of which also strongly impacts any life restoration, on land or swimming/diving. First, while the feet of hesperornithines are extremely Grebe-like, the rest of the hind limb anatomy is very similar to that of Loons (Reynaud 2005). Like Loons, hesperornithines had very long tibiotarsi, very short femora, and a high-angle hip socket with a very limited range of motion. Essentially, this means that the upper legs of Hesperornis were locked into a sprawl, which would have made standing upright very awkward. Loons rarely walk upright, and in fact I can't find any images online of such behavior. Loons also will push themselves along on their bellies, "flopping and dragging" as one site describes it (image above from birdinginformation.com)
Now, while the femur was basically immobile, it still had a role in contributing propulsive forces, as demonstrated by the arrangement of muscle attachments, which allowed it to conduct strong backward force through the leg. This is quite a feat because, (finally the answer to the challenge!) as in Loons, the entire, laterally projecting femur, the knee joint, and most, if not all of the tibiotarsus, was likely encased inside the body wall! Yes, according to some recent research (Zinoviev 2010), "the tibiotarsus...was held close to the body and was probably enclosed in the thickly feathered skin of the body wall". So images like mine, and the one below by Nobu Tamura (from Wikimedia Commons, CC licensed) showing free legs are wrong.
Like Loons (image of Common Loon above by Matthew Studebaker, from his photo blog), the feet stick out laterally from the very rear end of the animal near the tail, and it is the feet, rather than the leg as a whole, that provide most of the thrust and control (though, again, even the internalized leg musculature contributes to this).
So, congrats you those who noticed something wonky with the hind limbs! In all, hesperornithines were essentially super-Loons with Grebe feet, though their unique specializations for diving exceeded nearly all modern divers, making them possibly the most truly aquatic dinosaurs that have ever lived.
* Johnsgard, P. (1987). "Diving Birds of North America: 2 Comparative Distributions and Structural Adaptation. " Papers in the Biological Sciences.
* Reynaud, F.N. (2005). "Functional morphology of the hindlimbs of Hesperornis regalis: A comparison with modern diving birds." Geological Society of America, 37(7): 133A.
* Zinoviev, A. (2010). "Notes on the hindlimb myology and syndesmology of the Mesozoic toothed bird Hesperornis regalis (Aves: Hesperornithiformes)." Journal of Systematic Paleontology, 9(1): 65-84.