Sure, the gym is an easy way to find common ground with a potential mate, but that's not the intended purpose. Most people go to the gym to train, or at least they should. And even if someone is nice to you, it doesn't mean that they're comfortable with your advances. It just means they're afraid of hurting your feelings because you reek of desperation and it's sad.
Back Off, Buddy
If a woman has her earbuds in, a hat pulled down close to her eyes, and doesn't make eye contact with anyone (my wife calls it "bitch face"), she's probably not going to appreciate you going up and interrupting her in the middle of her timed set so you can suavely ask her if she's getting ready for a show, or something equally transparent.
Clearly, she's not interested in talking. If you cross that line be prepared to be labeled an asshole. And if she's married or is otherwise attached, you're causing yourself a problem you might not be able to get out of.
Leave the Front Desk Girl Alone
Don't relentlessly hit on the front desk girl. She's trapped there and she's paid to be friendly and nice to you. Don't take advantage of that and make her uncomfortable. It's a lame move and displays weak game on your part.
It Goes for Women Too
Ladies, if a guy is trying to focus on his workout consider leaving him alone. If he's not a douche, he'll respect you more when you focus on your workout too. Don't go to the gym to try and find a man, go there to better yourself. Flirtatiousness doesn't make you seem hot, it just makes you seem easy.
Now, some men and woman do go the gym just to look for hook-ups. They're pretty easy to spot. So you people just find each other, make some bad choices together, and leave everyone else alone.