Having read the paper, I should clarify that Dr. Naish and his coauthors Michael A. Woodley and Hugh P. Shanahan were not trying to explain all or even most "sea serpent" (SS) reports as pinnipeds, or even to prove that SS exist. SS identity was not the problem they were trying to solve.
They started with the question of whether there might still be pinnipeds left to discover and then looked at SS reports for sightings that might support the idea of unknown pinnipeds. They came away with the conclusion, based on statistical analysis, sighting reports, and other inputs, that there might be as many as three pinnipeds, all of them unusual and one truly spectacular, left to be discovered. One interesting inference is that we may have found all the “normal” pinnipeds (that is, the ones whose habits and appearance are what we expect for the order Pinnipedia).
You might say that what they did was take Dr. Charles Paxton’s statistical analysis of the "discovery curve" of marine animals over 2m long, which found there may be as many as 47 such animals yet undescribed (a figure he later revised downward) and apply it more narrowly, then add sighting data, to examine how many species in a certain group might be unclassified.
So to recap, this does not mean the authors are arguing all SS reports concern pinnipeds, only that a selection of what seem to be high-quality reports might refer to new pinnipeds.
The authors are to be commended for a new approach to the whole “mystery animal” question, creating a repeatable methodology others might apply to sharks, eels, whales, or other groups. It's not confined to marine animals. It could, for example, be used on birds, crocodilians, or primates, where it might shed an interesting light on the quest for unknown large primates that occupies so much of cryptozoology. (I found out I missed a publication from Michel Raynal that did apply a variant of this technique to whales, resulting in a predicted finding of 5 to 15 new species, the lower figure being not at all unreasonable given that we've had more than that described in the last two decades alone.)
Since I linked to Darren Naish's site in the first post, I link here to Cryptomundo for a sampling of the lively debate this paper has produced.