While I like the anatomical section, the phylogenetic section has a major issue that renders its results suspect. The authors state "we did not proceed to calculate a maximum agreement subtree from that set of MPTs because we have philosophical objections to the methodology behind that practice (i.e., removing OTUs from the final tree topology to seemingly improve resolution even though character data from the full set of included OTUs influenced the final results)." Yet that practice is near-universal for a reason- it allows you to use the most information to determine the topology. Taxa with unique combinations of characters can have major and unpredictable results on a tree, even if they themselves have an unresolved position. Then by a posteriori removing the less resolved taxa from the trees, you get to see what resolution exists while still utilizing their information. Remember, resolution is only important for displaying and understanding trees. A resolved tree is not more accurate or desirable than a less resolved tree, and if it's resolved by excluding data a priori, is objectively worse.
Instead, the authors undergo a series of steps I've never seen used before, which do nothing to increase accuracy. They start with only 54% of the initial data, which is virtually guaranteed to be a less accurate result than was generated by using the full dataset. Then they do tests to sequentially add taxa that result in the least amount of MPTs, under the mistaken idea that a more resolved tree is better. This leads to them adding 10 more taxa, so that now 71% of the initial data is being used. Again, nearly guaranteed to be less accurate than the initial results. Sadly, the authors never even tried to find the resolved topology from the analysis using 100% of the data, so we don't know what the results of their only worthwhile analysis was. I certainly don't trust Figure 10 to be an accurate reflection of the data, and because no TNT file is included in the supplementary information, I can't check what their data actually does say without tediously copy-pasting the matrix lines to construct my own TNT or NEXUS file.
Additionally, the authors state "2 OTUs representing individual specimens [NHMUK R3741 and NHMUK R1831] not previously assigned to a described taxon were excluded from consideration", but whether a specimen has been named or not should have no impact on whether it's included, as that's merely an accident of history.
The authors go on to compare their strict consensus trees with others' Adam consensus trees, but that can't be meaningfully done because of how Adams consensus trees are constructed. The point of an Adams consensus tree is that a taxon with multiple possible placements in the tree is put at the base of the most exclusive clade it belongs to. So if you had segnosaurs as either coelurosaurs or prosauropods in your trees, the Adams consensus would put them in a trichotomy with theropods and sauropodomorphs even though none of your MPTs had them in that position. Unfortunately, you can never tell from a figure if a taxon is actually basal or placed there due to conflicting more derived possibilities. Thus Dakotadon may be definitely placed down by Iguanacolossus in McDonald et al.'s (2012) Adams consensus tree, or it could have also been most parsimoniously found to be an iguanodontid or hadrosaurid for all we know. A reason I don't think Adams consensus trees should be used in general.
Finally, why not redescribe the vertebrae too, and illustrate the dorsals? If it's not done now, who knows how long it will be until Dakotadon is described again.
In conclusion, I implore you to use all of your data when determining phylogenetic relationships.