Very good question!
Here are some telltale signs of married men who are cheating and not being honest about it:
They throw around the words "discretion" and "discreet" a lot. (They usually misspell "discreet" as "discrete" for some reason.)
They make the assumption that you want the relationship to make up for something you are not getting at home (usually sex, or edgier sex), because that's why they are seeking the relationship themselves, and they assume that everyone has the same motivations.
They are reluctant to share a photo that shows their face clearly, or at all. It's one thing not to put a face photo up on OKC for professional reasons, but not being willing to share one privately even after some friendly dialogue is a likely sign of a cheater. If he is wearing sunglasses in ALL his photos, or his head is cut off or blacked out, be leery.
They don't want to meet you in person in a town they live in or work in.
They tell you their first name is John, and then two conversations later they admit it is really Steve. That one always makes me laugh.
Here are some things you can do to scare them off.
You can make it clear in your profile that you don't want to talk to such people.
Never meet anyone in person who won't share a cellphone number in advance of your first date. This will weed out at least some of them. (Plus you'll also be able to get in touch if you're going to be late or need to cancel.) And don't show up to the date unless you have called and actually talked to him first.
For your own safety, I wouldn't recommend sharing last names or any other personal info before you meet anyone in person, but once you have, then I think it is reasonable to request such things of each other. If the person won't tell you their last name AFTER you have met them, be leery. And once you have their last name, Google them. Find out their address and who else is living there if you can. And if you can't find a trace of them online even if they have given you a last name and a town, be leery.
If you are talking to someone you suspect is cheating but you aren't totally sure, make it clear to them that you won't hesitate to tell their wife if it comes to that.
And don't sleep with anyone quickly, certainly not on a first or second date. Take the time to get to know them. Don't pass out cybersex or sexy chat online to strangers, a lot of cheaters are ONLY looking for that, and will lead you on and waste your time just to get it.
For me personally, I will not get sexually involved with anyone who claims to be in a don't ask/don't tell situation, for the simple reason that there is no way to verify that they are being honest about that if the wife won't talk to me. I am sometimes open to being friends with such people if they are interesting and fun, since for a few, DADT is a step towards being in a truly open relationship.
And if you are still tempted to get involved with someone you know is cheating, just think about the fact that he is lying to the person he supposedly cares about most in the world and chose as a life partner, and is potentially exposing them to STDs without their knowledge or consent.
I hope this helps!