I correct my husband, because English is his second language, and he does want to speak English as well as possible, although he still sometimes gets annoyed that I correct him, but mostly he is receptive. I guess that is different than correcting a native speaker. And, I also would not correct a stranger the same way I correct him. The few times I have corrected a friend; it is usually because they are using a word that is not a word. For example orientated and irregardless. It is oriented and regardless (although one dictionary I looked up irregardless in said it was a synonym for regardless – sigh – and I guess orientated is accepted also, according to what I have been told, but I don;t know that or sure.
My girlfriend teaches college level courses and says she has students who write axe instead of ask. Come on now. But, my English is far from perfect also. I don’t mind being corrected, especially if it is a formal document, I appreciate it.
To @Trillian‘s point, sometimes people take offense to being corrected, when really you are trying to get to the actual meaning of what the person speaking to you wants to communicate. I agree, that is frustrating, when you are simply trying to clarify.
The different spellings in British and American English don’t bother me, English has all sorts of weirdness in spelling anyway, all sorts of exceptions. I don’t know if many other languages are like that, but Spanish for instance is almost always spelled exactly how you would guess by saying the word, not so in English.