Harry Potter
and the
Chamber of Secrets

House Elves

In this book, we meet our first house elf, Dobby. Dobby appears first appears out of nowhere, and when he's ready to leave, he simply disappears (with a loud crack). Of course, he's apparating and disapparating — terms that we don't learn until later.

We see Dobby later in the hospital wing at Hogwarts, where he again apparates and disapparates. However, in book 3 we learn that it's impossible to apparate or disapparate in Hogwarts or on the Hogwarts grounds. Apparently, this restriction doesn't apply to house elves.

Much later, in book 6, severe restrictions are placed on items that can be brought into Hogwarts by students. Harry keeps trying to figure out how Malfoy might have brought certain items into the school. One way would seem to be having a house elf bring something in to him after he's already inside. (I can think of at least two other ways.)

Prefects

In chapter 9, Percy the prefect deducts 5 points from Gryffindor when he sees Ron coming out of Moaning Myrtle's bathroom. In book 5, Ron and Malfoy are both prefects, and if prefects could deduct points, it's pretty obvious that Griffindor and Slytherin would both be well into negative numbers. So it's stated that prefects don't have the authority to deduct points.