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Burt has the head of the Graboid he killed in the first movie stuffed and mounted on his wall in the second. The Graboid that he and his wife killed by shooting it in the head for 2 minutes. Shouldn't it's head be in terrible shape?
It probably was quite messed up but a good taxidermist can piece together a nice trophy even from a horrifically damaged head, a common occurrence in the 19th century when hunting really big game since a head shot is safer than trying to hit the heart of a cape buffalo or rhino charging your ass. Its likely Burt paid for the very best considering it was the first Graboid he ever killed, and for all he knew, the last he ever would (which is accurate to an extent; even after two more movies and a series, he never killed another Graboid that actually had a head left to preserve).
Most of the damage Burt and his wife did to the Graboid was inside its mouth, anyway, where it wouldn't have affected the outer appearance as much. The only problem is that the Graboid's tongue-tendrils were effectively obliterated. But even this isn't a huge problem... there were several other Graboids that Burt was involved with killing to some extent. He may have been able to salvage the tongues out of the Graboid that dropped off a cliff, since that was probably all that could be salvaged. It'd make it a bit of a frankentrophy, but hey, better than being incomplete.
Salvaging the tendrils from the worm that fell from the cliff wouldn't work, though. That worm was "Stumpy", the one that lost a tendril trying to grab onto Val and Earl's truck early in the movie.
Actually the vast majority of the bullets struck the Graboid's "beak"... probably why it took so long to kill it, since they didn't do all that much soft tissue damage until the very end. And since the beak is already pock-marked and rough from hitting rocks while tunneling, the taxidermist probably just filled and buffed the worst of the bullet holes. The rest wouldn't have been noticeable.
Better question: what was the Taxidemist's reaction when he was given the chewed-up head of a giant sandworm to make into a serviceable trophy?
Who's to say Burt didn't do it himself? Given his extensive study of survival skills, taxidermy might have been among the ones he studied. Heck, a trophy like that might be worth learning the skill for on its own.
Even if he did have a taxidermist do it, there's nothing to suggest that the existence of Graboids was kept a secret. Hell, any taxidermist would probably jump at the chance to work on such a creature after reading about in the paper.
In the series all the scientists get worked up about dead skin cells and the like that lie on the bottom of the cave's floor when Mixmaster appears. However nobody seems that concerned over the fact you had a massive mutant wondering around outside the valley that was not only shredding small skin cells but massive hunks of it's shell. It's just woo, we caught the beast and the world is saved.
And it's stated that Mixmaster was in the water that was brought into Melvin's "lagoon". How many plants, insects, and birds made use of that water before the contamination was discovered. Containing the Mixmaster problem to Perfection Valley is a moot point, although probably great for Burt's survivalist training and monster hunting fees.
Why did Burt refer to the Graboids as "pre-Cambrian life forms" at the end of the second film? He didn't arrive until after the conversation in which the geologist identified the fossil as a Graboid-spike, and the creatures' ancient origins never came up as a topic of discussion again.
Burt may be a Crazy Survivalist, but I doubt he quite knows palaeontology. And, according to the Sci-Fi Channel, the Graboids and their ilk originate in the Devonian, not the Precambrian; there was certainly terrestrial organisms by the end of the Devonian large enough to sustain the Graboids, but there were only microorganisms during the Precambrian. So in all likelyhood, they're post-Cambrian creatures; beyond that is the realm of speculation.
In the original film, what happened to the body of Edgar, the power-company lineman whom Val and Earl found dead of thirst? They brought his remains to the doctor who confirmed the cause of death, but don't seem to have brought the corpse along when they moved on. The doctor couldn't have dropped the body off in Bixby, as the road got blocked and his vehicle wasn't suited to cross-country driving. If Edgar's body had been at the doctor's camp/building site, he and his wife seem awfully casual about it: a body in the desert heat isn't exactly going to be conducive to pleasant conversation, and leaving it far enough from their camp to not stink up the place would have been an invitation to coyotes. And it can't have vanished because one of the graboids ate it, because they can only detect moving prey.