Trivia: Check out the nurse that wakes Kristen up at the school infirmary. It is Robert Englund, out of his Freddy make-up. After Kristen wakes up, it is a different person.
Trivia: In the beginning of Nightmare on Elm Street 4: The Dream Master we learn Kincaid's dog is named Jason. Perhaps as a homage to the killer from Friday the 13th?
Trivia: The diner that Alice works at is called the "Crave Inn", probably a nod to Freddy creator Wes Craven.
Trivia: Scott Pierce is listed as a screenwriter. It really is a pseudonym of Jim and Ken Wheat.
Trivia: During the writing of the film, director Renny Harlin and some of the producers by chance happened to bump into famed director James Cameron. Cameron somewhat facetiously asked Harlin "How are they gonna bring Freddy back to life this time?" To which Harlin (also somewhat facetiously) replied "A dog pisses fire on him and he comes back to life." The idea ended up being used in the film, although in a more metaphorical manner than in a literal sense. (With Robert Englund explaining that the dog urinating fire onto Freddy's remains is meant to symbolize a Hell-Hound and how evil Freddy truly is).
Trivia: During production, the writers, director and producers couldn't figure out how to kill Freddy at the end of the film. Eventually, during a meeting, they discussed all of the possible ways to kill a villain or creature in a film. (Shooting, stabbing, burning, etc.) They then realized that all of the methods they were thinking of came from external forces. And they decided to do just the opposite - come up with a way for Freddy to be killed by an "internal force." Thus, the concept of Freddy's reflection cause the souls of his victims to revolt and tear him apart from the inside was born.
Answer: As Kristin was being burned to death in the boiler, she passed her ability to pull other people into her dreams to Alice. This enabled Freddy to get new victims.