NFL referees - The Zebras
What about “teh gay”?
I would consider “The District” as questionable, but “The Beltway” is definately more known. You will see it mentioned in national politics.
The Internets? 
Alcatraz Prison and the island it sits on - The Rock.
Muhammed Ali - The Greatest.
William Bonny - The Kid.
The police have many nicknames. One of them is “the fuzz”.
Joe Montana to Dwight Clark vs. Cowboys in '82 NFC Championship - The Catch.
The Broncos vs Browns in '87 AFC Championship - The Drive.
I’m guessing we ought to stay away from synonyms for diarrhea?
The annual Ohio State-Michigan football game is The Game.
As a spinoff to this notion, I’d like to call attention to a West Coast practice that gets used in movies and shows set elsewhere in the USA and which sticks out like a sore thumb: highways (mainly interstates but also toll roads and turnpikes) refered to as “the ___” with the blank containing a number, as in The 5 or The 10.
When that convention is applied to roads in the east, e.g.; The 65 or The 95, it sounds weird. In this area it’s mostly I-65 or I-95. not THE whatever.
Atomic / nuclear weapons were collectively known as The Bomb.
LeBron taking his talents to South Beach - “The Decision”
I was going to say this. Even though I live here, I still see it mentioned nationally. Not only in politics, but even in sports. For instance, even though Baltimore has its own beltway too, when Baltimore and DC play in sports (Redskins/Ravens, Nats/Orioles) they’ll often call it the Battle of the Beltway.
As for my own contribution, I’m surprised no one else has said it: The Pill. It’s so well known by that name that, even out of context, everyone knows exactly what pill it refers to, which may or may not be true for a lot of the other examples.
Major League baseball is “the Show”.
Menopause is “the change.”
The Finger
Some of my friends call facebook “The Book”.
Distance runners will find it at different places but all are aware of and have come into contact with “The Wall.”
and the Loop.
DC has “The Metro”. Never never call it “The Subway” unless you want to stick out as a tourist.
What about “the Border”? In many contexts, it’s clear what “border” you are referring to by context. For example, if you are in upstate NY, and ask someone, “Why don’t we go across the border this weekend?”, it’s clear that you are talking about going to Canada.
This building in London, UK, is referred to as “The Gherkin”.
(I thought it looked rather like a Faberge Egg when I saw it.)
" ‘IS HE THE GAAAAY?’ 'Well, god, Mom, I don’t know if he’s the gay. That’s a lot of pressure on one guy. He has to do the parade all by himself. “I’m here! I’m queer! …I guess I’m the only one.” ’ " - Margaret Cho