The paper contends that the dinosaurs developed most of their fundamental diversity back at the end of the Triassic and early Jurassic. This is important because there was a major revision of the terrestrial ecosystems during the Cretaceous. This was called the Cretaceous Terrestrial Revolution (KTR) and it brought about our modern ecosystems by and large. The root of it, ha! pun!, was that the angiosperms - ie flowering plants - evolved. Social insects and other critters radiated as well. The traditional thought has been that the dinosaurs were participating in this: there seemed to be a lot more diversity in the dinos during that time. The new paper questions this and actually states that the dinosaur diversity was more to do with the fact that there are far more readily available Cretaceous fossil beds. This created a sampling bias. It gave the impression that the dinosaurs were diversifying. Or so sayeth the paper.
It looks like an impressive bit of work. Sampling bias has been something I have had concerns about due to the fact that my main paleo interest has been mass extinctions. The severity of the extinctions can only be detected by what fossils are found before and after the events. If there are sampling biases simply because there are too few locales it can cause incorrect impressions of the event. More than one author has suggested that as more temporally contiguous fossil beds are found for certain mass extinctions we will need to do some major revisions to the body count. The main ones of concern here are the Permian (for the terrestrial environment) and Late Triassic.
One concern that I have is about my favourite archosaurs, the ceratopsians seemed to be diversifying alot (!!!) at the end of the Cretaceous. So too it seemed that the hadrosaurs were as well. However, this may have been a localized phenomenon in Laurasia. The ceratopsians of unusual size weren't out and about elsewhere.
Anyways, one of the authors, Dave Hone, has a blog, Archosaur Musings. It's worth a read.