Don't be an asshole. Don't do it. Do not insert yourself into the conversations of strangers, simply because you feel you could make a useful point, or could clarify something they've misstated.
It's bound to happen. You'll be sitting there on a bus, on in line at the coffee shop, or waiting in the dentist's office, and you'll overhear a conversation that relates directly to a strong opinion you hold, or an area of your personal expertise. You'll hear the strangers making factual mistakes, or wondering aloud about questions you could easily answer. You'll hear them make arguments that are plainly wrong for at least 3 reasons you can think of immediately. And you'll hear them serve up good-humored conversational softballs to which you could respond with any number of funny quips.
You will want to butt-in. The urge may be so strong that it seems irresistible. You will rationalize it to yourself. You'll think "These guys will be thrilled that they just happened to pose questions in earshot of someone who knows the answers! It's their lucky day!"
But you are dead wrong. You are setting yourself up to look like an insufferable prick, and the only thing you will make the strangers feel is a secret desire that you drop dead.
Imagine talking to your friend on the crosstown bus:
You: "I heard KFC's grilled chicken actually has more calories than the original recipe."
Friend: "You don't say?"
You: "Yeah, it's cause of the marinade."
(Suddenly, Colonel Sanders himself turns around from the seat in front of you)
Colonel Sanders: "Actually that's not true. The grilled chicken only has 2/3 the calories. And it doesn't even have a marinade."
You: "Fuck off, Sanders."
The more you know about the topic, the more you will feel compelled to butt in. This happened to me last week at a bar. The strangers were discussing a movie that happened to be one of my favorites. They were arguing over the fine points and they couldn't remember certain details. It was a fun, jocular conversation, they were laughing, and they were making lots of little errors in talking about the film.
I sat there and I knew what I had to do. I had to keep my mouth shut. I could have lectured them for 20 minutes on all the fine points of the film. I could have delivered an impromptu symposium on it. But the conversation - and this is what you have to understand - the conversation they were having was not really about the movie. The movie didn't really matter. What it was really about was a couple of friends unwinding after a long work day and sharing a couple of beers. Having a few laughs. Enjoying some good company. Even though we were in a public place, there was an expectation of privacy. And if it just so happened that their casual banter involved talking about a movie - and not even getting it right - then that was their prerogative. They couldn't remember the actor's name? Didn't matter. They were having more fun trying to figure it out than they would have if I butted in like a google search result.
There are circumstances I guess where you can break the rule and butt-in. If someone gives bad directions, or someone is about to get on the wrong train, then it's okay. If you can be a good samaritan and save someone from headache and inconvenience then do it. But otherwise stay out. Allow the strangers to say things that are wildly incorrect. Allow them to be offensive.
One of my goals in life is to write a book. And the reason is because I want to someday be tempted by the ultimate butt-in scenario: some strangers talking about my book while I am sitting right there. The urge to say "Actually, I wrote that book." will be so overwhelming, that by resisting it I might break out into sweats and the shakes - but it is the ultimate test. Because anyone who says "Actually, I wrote that book." is a douche. And that's the question you have to answer. When push comes to shove, when all the chips are down: will you respect someone's privacy? Or will you be a douche?