At least once a day, someone I know will post something to Facebook which I'm 99.9% certain has been proven wrong. Several times a day someone will post items that I'm fairly certain would fall apart under a 5-10 minute Google hunt. You might suppose that I, being the ever-vigilant skeptic, would be the first to comment, tearing their post apart.
In an ideal world, a person who takes the time to post a link to their friends should absolutely appreciate someone else providing feedback and evidence which says "Hey, that's actually not quite correct because of extremely verifiable reasons x, y, and z."
However, this is far from an ideal world. The things people care enough to post to their friends are often things the person has incorporated into their own identity. Chances are, the person didn't just stumble across some a random page and it convinced them of some dubious topic; it's much more likely that the person already cared about said topic, and is looking to evangelize it to others.Example? I'm fairly certain vaccines are not bad, and are in fact a very good thing. Am I convinced drug companies are benevolent and there are no risks? No, of course not, but the vast preponderance of evidence available leads me to believe that vaccines work, and the risks are very small (and much much much smaller that the risks of the diseases, even the "harmless" diseases).  But, I also know that when someone posts a link to an anti-vaccination article, there's very little I can say or link to in a comment that is going to change that person's mind. There are many reasons for that, and there are many reasons why good evidence should change their mind, but the biggest reason it's not going to is because you're on Facebook.
If you were sitting in a café or at a kitchen table with the other person, there's opportunity to read body language, facial expressions, and tone of voice, and there's no crowd of onlookers. If you were writing emails to each other, there'd be time and space to fully and calmly develop your argument. But when you challenge their idea on Facebook, you've called them out as wrong in front of their friends, family, and coworkers, and they might feel it as a personal challenge. No matter how nicely-worded your response, you are in effect saying "You're wrong, you idiot!" in front of a crowd of their peers. And, given they probably feel deeply about the issue, you've publicly insulted part of their identity.
What to do?
Well, how are we to fight the good fight? How do you effectively spread correct information in the face of incorrect?
First, know your goal.
Ask yourself why you want to respond. What do you hope to achieve? The best I can figure, there are (at least) three general motivations for wanting to debunk an idea:
1) To convince the person the idea is not right.
2) To convince other people the idea is not right: i.e. prevent the spread of Facebook/forum misinformation.
3) To insult and belittle them or the idea, or make yourself seem superior.
Or some combination thereof. Which is your purpose? The first two are compatible with each other, but the third option usually takes the others off the table. If you merely want to make fun of someone or "score points" for "your side", fine, but, after that, know you will have basically zero chance of convincing that person they might be wrong, or anyone else who doesn't already believe you.
Second, pick your battles.
You probably won't convince someone about vaccines on Facebook, because chances are they're deeply invested in their beliefs: they've made decisions and spent money and time based on the belief, and are not looking to get told they made poor choices in front of their peers, so defensive mode kicks rather quickly and firmly.
This is not to say you should never try the hard issues, just that their nature requires more thought and tact (unless you merely want to insult them).
Third, pick your venue.
Facebook is tricky. Dozens or even hundreds of their friends and family could be reading. Even the most sincere and humble counterpoint can seem like a scathing slur. Other people jumping in, the small writing space, and no formatting options make things difficult to follow. And everything is public.
Email or private messages are better. That removes part of the "public attack" dynamic and the possibility of others jumping in.
But, that doesn't immediately help if you want to counter the public spread of a piece of information. It could help in the long run if you convince the person, or at least help them believe it not so firmly/evangelistically. If you do stay public, be as tactful and thoughtful as possible.
Fourth, don't call them dumb or evil.
Never make it seem like you think they are dumb for falling for misinformation. Most people aren't experts, and most people aren't stupid. Most likely, it's just a case of them believing something that is not true. Given the internet, it's easy to find "confirmation" of most any idea you care to name, and so unless a person is actively looking to disconfirm their belief, they'd never know.
Instead, emphasize that it's a confusing and complex issue (because, most of the time, it is). Point out that, though the evidence might be complex, the majority of evidence does seem to lead away from their conclusion, or at least does not confirm it as easily as they might think. Don't try to come off as an "expert" (even if you are): it'll just make you seem arrogant, it won't help, and they can easily find hundreds of other "experts" who support their belief. Always go with evidence over authority.
Finally: make sure you are right / promote general rationality.
Don't be afraid to disconfirm your own stance, publicly and privately. Is this just a matter of opinion, or is there real evidence? Don't be afraid to say something is uncertain. Rather than debunking their idea in favor of something else, it's OK to say "there's not enough evidence either way". It's OK to admit that doctors often don't know what they're talking about. It doesn't mean the other person's idea is correct, it just means no one knows the correct answer, or it's not simple.
Always follow the evidence, even if that means admitting there's no good evidence.
Gentle skepticism is not easy, and is not guaranteed to work, but it beats "scoring points" by ridicule, intentional or not.