Saying "Good Morning, How do you do? That is a very fine hat you are wearing." to your friend. It's accurate in intentional meaning, but the level of formality is inappropriate. You'd say "'Sup, Rosie? Nice hat."
Another example could be: "I get pleasure from calling my Grandma daily." It is a little formal, but more importantly is the use of "pleasure". "Pleasure" means "it makes me happy", which is accurate, but it also has the connotation of physically feeling good. So the sentence would have the second meaning of getting sexual gratification from calling your Grandma. That would be inappropriate. You would say "I like calling my Grandma everyday."
It's also the same thing with the word "gay", which means "happy" as well as "homosexual". It's only ever used in poetry, really, because although it's accurate to say "I feel gay today" to mean you're happy, most people would immediately think of homosexuality, and wonder why you chose the word "gay" to talk about being happy. You could stick to the word anyway and laugh at people's reactions "Oh I feel so gay today! Don't laugh, you know what I mean! Elated! Ecstatic! Frolic-some! Happy! I feel like skipping through the meadows like a carefree lamb! 'Gay' sums up exactly how I feel about today!" or if you didn't want to make a joke about it, you could just say "I'm in a good mood today!"
I guess a lot of times, words or phrases would be inappropriate because they have a double meaning or because they're the wrong level of formality. They'd understand your meaning, so they're accurate, but they're not appropriate.