Between the interview and the job offer come the reference and background check. Background checks are easy enough. You just need to verify that the person has the degrees he or she claims to have, that they don't have any surprising criminal history (any relevant convictions should have come up in your application process), and, if relevant, you want to make sure their credit is good enough. If all those things check out, it's time to speak with actual other humans about your your job candidate.
Reference checks are generally necessary to lessen the chances of making a bad hire. (You can never completely eliminate the risk of bad hires.) After all, you don't want to hire the guy who embezzled from his last company, nor the woman who was fired for sexual harassment. But, there are sometimes you should think twice before taking a reference at face value.
You found a former boss yourself, and this person's account varies dramatically from the other references. In today's connected world, it's pretty easy to find someone's former boss, even if the job candidate didn't helpfully list it for you. So, you call up and say, "I'm considering Jane and..." and the person goes off into a rant on how Jane is the craziest, most horrible person you will ever find. Now, is this possible? Of course! But is it also possible that Jane is a perfectly wonderful person, and this former boss is the totally awful one? Yes. If you call three people and they all agree that Jane is a nightmare, believe it. If two people say she's awesome and one goes on a rant, you may want to disregard the bad reference.
The bad things aren't bad for you. The things that made someone a nightmare employee for one company could make them an ideal employee for you. If the job you're hiring for is substantially different, it may be that those bad "skills" won't make a whit of difference to you. In fact, someone who made a lousy accountant may make a superior marketer. Keep that in mind when you're asking questions.
You don't know the reference at all. One huge advantage to hiring through networking is that you know people who know your candidate. When you've plucked someone off the internet, you don't have much to go on. So, you take a look at the candidate's resume and notice they didn't list a boss from their last company. You call that company and track down the boss, only to be given a bad reference. But, you don't know this person. At all. Are you sure you want to reject an otherwise great candidate because of one person you've never met?
The negative reference is actually positive. Great managers try to hire people who are smarter and better than they are, so that the company will thrive. Bad managers? Well, they are intimidated by good people. If you ask, "How was Jane as an employee?" and the answer is, "She thought she was so smart. Always taking on new projects," well, that can go two ways. It's possible that Jane didn't respect boundaries and roles. It's also possible that Jane was just better than the manager and the manager resented her. Consider that possibility.
The negative things are protected by law. Reliability is important, no doubt. But, if the previous manager says, "Jane called out a lot," you need to follow up with, "Did she say why?" If it was due to a disability, or legitimate intermittent FMLA leave, you need to disregard that at your own legal peril. Smart candidates won't tell you about a disability until they have the job offer in hand, but you'll still be violating the law if you find out about it on your own and then make your decision based on that.
The bad things were a long time ago. Did you ever do something stupid? Were you once clueless? Did you walk out mid-shift at Burger King at 18? Swear at a customer when you were 22? Well, so did some of your candidates, but hopefully they grew out of it--just like you did. If it was 10 years ago, it probably shouldn't be relevant as long as things have been good since then. This goes for minor convictions as well. That DUI 10 years ago--with a spotless record ever since--deserves to be disregarded.
Everyone wants to find the perfect employee. Reference checks can help you do that, but make sure you don't just blindly believe everything someone on the other end of the phone says.