Wikipedia says that Dee only affected the poor inhabitants of that diner, but I'm pretty sure that Dee's actions have effects on a larger scale than that. On page 11 of the comic, a news report shows "his jewel in action":
The Sandman #6 page 11
And on the next page:
TV: "...nightmares, sleeplessness and insanity reported earlier on local news is shaping up to be a planet-wide phenomenon."
Additionally, several large disasters are shown on the opening pages of the next issue (#7 "Sound and Fury"), including a hospital on fire and an airplane that crashed on a freeway.
Some Justice League members, John Constantine, and other DC characters receive cameo appearances (or more) in Preludes and Nocturnes, so this takes place in a (the?) universe with mainstream characters. I would imagine that the superheroes or JLI in this world would attempt to mount some sort of response to this catastrophe.
Were the events of "24 Hours" shown in any other comic?