As one of the authors of the paper in question, I'd like to point out that the headline and summary are very misleading. We have *not* identified any particular miscalculation and nor have we claimed to. Indeed, we are impressed by the recent safety report and agree that it is very unlikely that there will be a disaster.
The basic point of our paper is that what we really want to know is the chance of the disaster happening, but the reports give us the chance of it happening given a large number of physical assumptions. These probabilities are not the same, because there is a small but real chance that there is a flaw in these assumptions. This need not be due to any mistake on behalf of the physicists but may be like Lord Kelvin miscalculating the age of the Earth because nuclear fission and fusion were not yet known. Think of it this way: in a random sample of 1,000,000 cutting edge scientific articles that look as reliable as the LHC safety report, how many of them are likely to have flaws that invalidate their reasoning? This is especially pertinent as the safety report for the LHC's predecessor (the RHIC) failed to take into account anthropic considerations.
Of course even if the argument is flawed, we are still probably safe. We have indeed dealt with this point in the paper. The overall risk is very small, but larger than the raw calculations suggest, and non-negligible when there are 6.5 billion lives at stake. We thus urge caution and a reassessment of the safety of the LHC taking these considerations into account.
I encourage you all to read the actual article, which goes into many of these points in detail: