There are several important aspects of an eatery that classify it as a diner. Simply slapping the word "diner" in the name of the establishment doesn't cut it, either. First, there needs to be a long counter with stools at which individual customers can sit and eat. This is ideal for the quick "coffee before work" or "break from work" stop, as well as being convenient for a quick bite; something small like a club sandwich, or a pastry.
Then there are the actual sit-down areas. A true diner should have enough booth seating to accomodate all patrons. Table and chairs don't really work, and they're usually awkward in their placement. You shouldn't find such seating in a diner; booths are a necessity, as illustrated by the next requirement.
Mini-Jukeboxes. At every table. This is the single most important diner element. Not to overlook the necessity of the stools and counter, however, because if a restaurant has one and not the other, it ain't a diner. Traditionally, you have the selections in a window (which are flipped through via a turn-dial at the top), and two rows of buttons at the bottom through which you enter your selection - usually the top row is letters, and the bottom row is numbers. Musical selections aren't really standardized, however Sinatra, Elvis, Jones, etc. seem to be de facto.
And no diner would be complete without a good old-fashioned soda fountain. No, not these mechanical things that you press your cup on the lever and it dispenses soda found at every 7-11 and Circle K in the country. I'm talking about an honest to goodness soda fountain operated by an honest to goodness soda jerk who mixes and carbonates your soda on the spot.
There are also a few extras that aren't required for a diner to be a diner, but add lots of points to the atmosphere.
First, there's chrome, neon, and stainless steel. Lots of it. The sides of the stools at the bar, the railing of the bar, trim along the lights and windows, foot-rails, the mini-jukeboxes; anything short of stuff on which customers sit, or food is served can be made of, or contain chrome. Anything made of glass should have neon reflecting off (or through) it at some angle.
Of course, chrome is also a predominant element in diners that have an automotive theme. These diners typically consist of bright, even deco-like colors, checkered flags, and in some cases, the booths are replaced with classic car bodies. Note, that while many diners contain a floor consisting of a black and white checkered design (which also adds points), that doesn't mean it's an automotive-themed diner.
Then, there are the extreme extras. Things like rollerskating waitresses, window-mounted serving trays for eating in your car, vintage equipment on display (gas pumps, soda machines, and the like), retro memorabilia, and other nice touches. You'll also find that many true diners have atomic elements scattered about. The diner exploded in popularity during the fifties, which was around the same time atomic energy was getting widespread attention (even calling the period "The Atomic Age"), so you'll see the well-known swirls-orbiting-a-nucleus atom design pop up occasionally.
The bottom line is, you can't really call a place a diner without the aforementioned necessities. It has to have a 1950s feel to it, and shouldn't contain even the smallest trace of corporate-owned cookie-cutting. Generally, they're not chain-owned, so each one is going to be pretty different, while still containing the same elements. I have yet to see a diner that is part of a chain or franchise, so I'm pretty much certain that a true diner is individually owned and operated.
Now you have facts to back you up when you walk into an imitation diner and scream "This isn't a diner!" at the staff.