I haven't seen a particular critique of that paper so can't comment.
Bigger picture, I wasn't commenting on the particular validity of that paper as much as what this type of study could tell us...hindsight I should have picked an example from another disease.
Unfortunately that paper became my litmus test for people arguing from bad faith as it was such a darling of the "COVID is just the flu!" crowd. My memory of the main problem was that the confidence interval of the false positive rate of the test used included values higher than the entire positive rate of the sampled people. I.e. they didn't have enough data to rule out the claim that no one had COVID antibodies, let alone to justify that such a shockingly high percentage of the population could have had them already. Here's a random overview of the critiques that I found on google just now:
Anyway, I'm sure better data exists at this point. The CDC survey data you linked to looks very interesting and seems to (with caveats) put the percent-immune at 16% or less as of a few months ago. It's sort of a middle ground with what the article here was claiming - 100 million immune Americans still seems to high but not by that much so given how cases have continued since the last serological survey results.
Bigger picture, I wasn't commenting on the particular validity of that paper as much as what this type of study could tell us...hindsight I should have picked an example from another disease.