Quote 1
"And now, sir," continued the doctor, "since I now know there's such a fellow in my district, you may count I'll have an eye upon you day and night. I'm not a doctor only; I'm a magistrate; and if I catch a breath of complaint against you, if it's only for a piece of incivility like tonight's, I'll take effectual means to have you hunted down and routed out of this. Let that suffice." (1.16)
Doctor Livesey is a local judge as well as a doctor. In that capacity, he has words with Billy Bones after a run-in at the Admiral Benbow Inn. Because they operate at sea, we rarely see pirates coming up against actual agents of the law. Who in this novel seems most afraid of legal punishment? Why?
Quote 2
"Most likely Trelawney's own men," said the doctor; "those he had picked up for himself before he lit on Silver."
"Nay," replied the squire. "Hands was one of mine."
"I did think I could have trusted Hands," added the captain.
"And to think that they're all Englishmen!" broke out the squire. "Sir, I could find it in my heart to blow the ship up." (12.37-40)
Squire Trelawney's patriotism blinds his judgment. When Long John Silver tells Trelawney that he lost his leg in a battle under Admiral Hawke, Trelawney believes him. Here Squire Trelawney is disappointed in the pirates not just because they want to murder him, but because they are all Englishmen. Squire Trelawney's idealism makes him an easy mark for Long John Silver, which is perhaps meant to be a jab against idealism.
Quote 3
There was not a breath of air moving, nor a sound but that of the surf booming half a mile away along the beaches and against the rocks outside. A peculiar stagnant smell hung over the anchorage--a smell of sodden leaves and rotting tree trunks. I observed the doctor sniffing and sniffing, like someone tasting a bad egg.
"I don't know about treasure," he said, "but I'll stake my wig there's fever here." (13.10-12)
According to 18th century medicine, fever is mostly caused by bad air, hence Doctor Livesey's concerns. There is foreshadowing here in the fact that the first glimpse of the island is automatically associated with sickness. It's as though the treasure itself were making people sick – certainly, it's going to make people crazy. The "fever" the doctor smells could just as easily be gold fever, which will drive nearly everyone on the island to madness and murder before the novel ends.