Quote 1
Dr Seward's Diary (Kept in phonograph) (5.16)
Dr. Seward keeps his diary in a phonograph, which is an early recording device. All he has to do is speak into it and his words are recorded. Mina offers to type out the recorded entries later, which is (supposedly) how they came to be included in the collection of documents that form the novel. Check out "Best of the Web" to see a picture of a phonograph from the 1890s.
Quote 2
"Good God, Professor!" I said, starting up. "Do you mean to tell me that Lucy was bitten by such a bat; and that such a thing is here in London in the nineteenth century?" (14.76)
It's funny that Jack Seward has no trouble believing that a vampire bat could exist—he just has trouble thinking that it could exist in his ultra-modern, super-civilized, 19th-century London.
Quote 3
[…] we recognized the features of Lucy Westenra. Lucy Westenra, but yet how changed. The sweetness was turned to adamantine, heartless cruelty, and the purity to voluptuous wantonness. (16.17)
Jack Seward can't believe how much "Lucy Westenra" has changed—he keeps repeating her full name, emphasizing that it's now just an empty label. "Lucy Westenra" is no longer herself; this over-sexed she-demon is not the girl he fell in love with. This vampire lady might be sexy, but she's sexy in a totally freaky way.
Quote 4
If I don't sleep at once, chloral, the modern Morpheus—C2HCl3O.H2O! I should be careful not to let it grow into a habit. No I shall take none tonight! I have thought of Lucy, and I shall not dishonor her by mixing the two. (8.35)
Chloral, or chloral hydrate, is a sedative that was originally used to treat insomnia, and sometimes used as an anesthetic. It's only mildly addictive, but it was still abused and misprescribed a lot in the late 19th century. Nowadays it's illegal in the US without a prescription. In the late 19th century, though, it wasn't a controlled substance, and doctors, like Jack Seward, could just dose themselves if they had trouble sleeping. No wonder addiction was so common!