Your employer is going to check up on what kind of employee you are. He can't just go by your own statements, as many people outright lie. So he might call your references, look you up online, and generally dig a little bit.
If the job is one where security or money is an issue, he might go so far as to get a private investigator to do a background check. Look up your prison records. Your school records. Anything written about you.
In general, I expect that a bank should not hire you if they see that your Facebook is all about you and your gambling problem. A police department should not hire you if your Facebook is all about your collection of explosives and drugs.
That said, you should do the same thing. Check up on your employer as a company for workers' rights abuses and complaints. Check the Better Business Bureau. If the dude is the business owner, like for a franchise or a small business, check out his background online. Prior business activities may show him to be an awful person. Maybe he has a criminal record that you're not morally comfortable with.
But in this economic climate, the supply of jobs (especially decent jobs) is limited, and so you're lucky to get anything. And in general we think of the employer as being the one who can afford to be picky even when there isn't a depression.
For these reasons, it's important to leave your real name, phone number, email, etc off your profile. Without that it's difficult for the employer to find your Facebook profile, but it's also more difficult for long-lost friends to find you. And that's part of the point of social networking sites for some people.
If you decide to put up your name in your profile, then don't put embarrassing bare-ass pictures on it. Or if you do, you have no reason to be upset when someone looks at them and judges you for it. On one hand, your employer has your word that you're a good employee. On the other hand, he has proof that you're a vodka-swilling exhibitionist. In the balance it comes out to a negative for you and he might choose someone else.
In general, I hate the idea tht anyone knows anything about me except what I tell them. I don't want a credit score, or a tax history, or a driving record, or whatever. I want my school to record only that I attended from this month to this month and that I graduated with this degree. If someone wants to know something, they just have to trust that I'm telling the truth. Just for me though, society wouldn't work smoothly if everyone had the luxury of that anonymity. But as an American I'm used to demanding luxuries that I categorically deny anyone else. ;P