Is it ever worth the time and effort to correct someone else's grating grammatical mistakes?

There is nothing wrong with having gut reactions to the way that people say things. I am completely aware that the standard/educated version of a language is arbitrary (i.e. is no more "correct" in any real sense than any dialect), and even still, I have pet peeves and things that irk me about people's language usage. I think these are unavoidable, just like my reaction to certain fashion choices that people make in their outfits. But, like with fashion, there is very little objective truth to my judgment about any of it.

I try not to actually challenge people on uses that bother me; aside from the arbitrariness of language, every bit of evidence suggests that stopping language change in any significant way is like going to the beach and trying to stop the tide from coming in. There was a more in-depth discussion about this in a previous question.

That said, I do believe there is a certain time and place where standards and clarity are important. In formal contexts, information is often supposed to be presented in a certain way, and, generally, these conventions benefit everyone. Also, following certain language conventions in these situations can eliminate ambiguity. If I am asked to proofread an academic paper that my colleague has written, I would make corrections for things that I would never object to otherwise.

Does the grammatical faux pas compromise or endanger the communication, or is it merely annoying? (Annoying to you personally, of course. The speaker, and no doubt many others are perfectly happy with it.)

Language can be a delight, but it is also, and to many, merely a means to an end. If you are with friends who enjoy language for its own sake and who want to improve their understanding and usage of it, a courteous and appropriate correction will be appreciated.

If you are with strangers or persons with whom you have only a business relationship, then as long as the communication is not jeopardized you're probably best advised to bite your tongue and realize that you are a member of a small minority.

Unless, of course, you really do wish to be viewed as a snob.

In addition to the other good comments posted, I'd say that familiarity should probably be a major factor in determining the best course of action.

I might wince, but generally I'd let these 'mistakes' pass without comment, unless I felt particularly familiar with the person speaking. A casual acquaintance or an general colleague will go unmolested, but a family member, a close friend or colleague will more readily be 'corrected'.

In the case of my wife, saying "We was doing this or that.." (**), I throw myself to the ground, kicking and shouting "WE WERE.. WE WERE!", not that it seems to do any good. OK, I'm joking, but I've been sorely tempted! ;)

** I (snobbishly) used to think it was a sign of a poor education, but in the case of my wife it isn't - it's a regional thing. A lot of people in the area we live say it, and even worse, none are seemingly even remotely aware of the fact!

Many people take offense when you try to correct their grammar or pronunciation (or spelling, in a written document). Given that it's impossible to tell just how offended someone might be, and given that many people aren't likely to change how they speak even if they accept your correction, I recommend biting your tongue unless you know the listener wants your feedback.

I have a coworker who mispronounces words all the time. He is a native speaker, but certain words are just wrong in his mouth. The most grating is when the mispronunciation leads to a different word (my worst peeve: he says aTTRIBute instead of ATTribute, which makes it a verb instead of a noun). But if I correct him, will he get upset? Best not risk it.