Yeah, there are many problems with the paper. Its descriptions of previous work is often inaccurate. For example, it cites ref. 49 to claim that Y chromosome diversity is smaller than previously believed. Ref. 49 doesn’t say that at all, and in reality the relevant Y chromosome diversity – the length of the oldest branches – was shown in 2013 to be much higher than previously thought, when a new, highly divergent branch was discovered.
Other examples: Sanford’s paper on waiting times in hominids does not show that that hasn’t been enough time since human-chimpanzee speciation for evolution to work (unless you make idiotic assumptions, that is). Haplotype blocks, to the extent that they’re a real thing, cannot be explained by single early instances of recombination; since their first description (their ref. 60(*)), their characteristic feature has been that multiple recombination events were required at their ends, to break up multiple haplotypes.
More seriously, the paper simply does not address the actual genetic evidence for a large ancestral population size. As we have discussed previously in another thread here, you can inject any amount of genetic diversity into Adam and Eve, but that diversity won’t look anything like the actual diversity we see. What we see has a characteristic frequency distribution that falls off as 1/frequency, so that there are many more rare variants than common ones. Genetic variants in Adam and Eve would all be at high frequency, since the lowest frequency variant you can have with 2 individuals is 25%.
The other strong piece of evidence that human genetic variation is the result of accumulated mutations is that it looks like accumulated mutations. That is, kinds of mutations that we know happen very frequently also appear very frequently in modern genetic variation, and kinds of mutations that occur rarely are seen in variants. (Strikingly, exactly the same pattern is also seen in genetic differences between humans and chimpanzees. My prediction is that you will never see a creationist address this simple fact.)
Really not a good paper.
The second paper strikes me as nuts, by the way: complete overkill in fitting out a highly detailed model when they have no idea whether they can get the coarsest features right with their proposed solution.
(*) I will note that I was, for inexplicable reasons, included as an author on that paper, to which I contributed very little. (On the other hand, I worked my butt off on ref. 61.)