A plesiosaur was found by a Japanese trawler

Claim

In 1977, a plesiosaur carcass was netted by the Japanese trawler, Zuiyo Maru.

Swanson, Ralph, 1978. A (recently) living plesiosaur found? Creation Research Society Quarterly 15(1): 8.
Morris, John D., 1999. Dinosaurs, The Lost World, & You, Master Books, p. 38

From the description, the corpse (which was thrown overboard almost immediately after its picture was taken due to its unbearable stench) was very probably that of a basking shark that had died and decayed, with the lower jaw preferentially rotting off first, thus exposing the braincase, leaving the suggestion of a long-necked head. This is a common feature of basking shark carcasses.
Even if it were a plesiosaur, the existence of such a carcass would say nothing about evolution's truth or falsity; plesiosaurs are thought to be extinct because of the lack of living specimens and the age of existing plesiosaur fossils, not because evolutionary theory predicts that plesiosaurs ought to be extinct. Species thought to be extinct -- coelacanths, among others -- have been rediscovered without contradicting evolutionary theory.
Identical carcasses of such "plesiosaurs" have been found, and examination of tissues, as well as the presence of an entirely cartilaginous vertebral spine, only 7 cervical vertebrae (fewer than even the 10 to 13 cervical vertebrae of short-necked plesiosaurs, aka pliosaurs), and the total absence of a pelvis suggest that these carcasses were once basking sharks, and not plesiosaurs.
Creationist think-tank Answers in Genesis agrees that this claim is false, and is on their list of arguments that should not be used.
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Exclusion (the basking shark explanation is left out)
Hasty Generalization (if one species is not extinct, that doesn't mean no species is extinct)
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Kuban, Glen J., 1997. Sea monster or shark? An analysis of a supposed plesiosaur carcass netted in 1977. Reports of the National Center for Science Education 17(3): 16-28.