After reading some responses suggesting the authors don't understand how to measure superconductivity, I double checked the senior author's credentials. He is very much a legit scientist but seems to be a relative newcomer to superconducting. There is a long established history of respected and productive scientists entering fields they don't really know anything about and engaging in mild to moderate quackery. In this case, I am now fairly confident that the following is true:
* he and his team did discover a (probably) novel diamagnetic material.
* it may or may not have interesting properties
* however, it is not superconductive.
According to people who were able to more fully read the "real" paper, the key issue is that their measurements, if taken at face value (and not as due to, e.g., bad contacts with the material) suggest two contradictory things:
* the sample is extremely pure (due to the shape of the first graph).
* the sample has impurities causing it to not exhibit zero resistance, and not to exhibit "full" superconductive properties (i.e. having zero resistance under a magnetic field with increasing strength).
Additionally, since they were never able to measure Tc, they can't show the full Meissner effect as that requires heating up the sample to above its Tc first and then cooling it and flipping it, something you can't do with a diamagnet. By itself the fact that they didn't reach this temperature did not bother me, because I assumed that the senior authors were experts in superconductivity and had made sure that the material simultaneously exhibited other superconductive properties like zero resistance (or close enough when factoring in impurities). The fact that they were so focused on replication and the process was so simple made it unlikely to be fraud.
But, the fact that the first chart doesn't make sense unless the sample were completely pure, plus the lack of expertise they have with superconductors, indicates that it is much more likely measurement error on their parts, in which case it's not clear whether there's any evidence at all for superconductivity right now outside the diamagnetism. Given that there are many room temperature diamagnets known (albeit perhaps none as strong as this one?) and no room temperature superconductors known, this puts the odds that this isn't a superconductor at practically certain, IMO.