The image above is Haeckel's famous drawing of embryos, a series of images which he presented to illustrate his now discredited notion of recapitulation. He fudged the details to make the whole thing look more convincing, which was undeniably a bad choice.
This figure was reproduced by some textbooks as an interesting and historical demonstration of broad similarities between related species especially in their early development, a pattern more similar to von Baer's laws than Haeckel's ideas. Nonetheless, creationists like Jonathan Wells like to complain about teaching evolution because of this figure's dubious history. Wells does not contend that the pattern itself is invalid. He can't. And most modern textbooks have stopped using this figure, replacing it with photographs of the same embryos or with drawings from photographs.
That style of illustration is shown in the second image here, copied from this post by the Discovery Institute's John West. You'll note that, despite West's claim that this is "a version of Haeckel's drawings," they are actually quite different in their details. These are clearly redrawn photographs of actual embryos, and as such do not bear the taint of any errors Haeckel made, intentionally or otherwise. Trying to smear biologist and filmmaker Randy Olson because West doesn't understand the subject is hardly honest.
West also lies when he claims that "Haeckel’s diagrams are on their way out because of the efforts of Darwin’s critics." Stephen Jay Gould wrote a whole book addressing not just the technical issues with Haeckel's drawings, but the philosophical and biological problems with Haeckel. It wasn't critics of Darwin who spiked Haeckel's drawings, it was critics of Haeckel.
Randy Olson's Flock of Dodos will be shown at KU's Woodruff Auditorium on February 12, at 7:45, as part of KU's Darwin Day celebration.
I know, I'm more than 2 years too late, but there are still discussions in the internet whether Haeckel's drawings are in modern textbooks or not.
You said "You'll note" but I do not see much difference, and the DI says there is none.
I could not find out, which details you were talking about.
Of course, the Discovery Institute also never stated which particular errors of Haeckel's drawings are still in the textbooks.
The only detail I heard about is the tail of the human embryo in the lower left corner. It is too long in Haeckel's drawing but significantly shorter in the textbook version.
Is this one of the different details? Are there more?