Ok, this is a bit nitpicking, but who cares? This page is about complaints I have, so I complain.
The word "irony" or its derivation "ironic" is one of the most abused words in many languages, but especially English. It's very often used in situations where its meaning just doesn't fit.
"Ironic" does not mean "funny", "curious" or "interesting", even though some people seem to think that it does. You cannot replace the expression "that's funny" with "that's ironic", or the expression "curiously" with "ironically" (except when the usage of the word corresponds to its true meaning, of course).
The most basic element of irony is juxtaposition of opposites. It's always about opposites. For example, if someone attempts to do something, but the exact opposite happens instead, that is ironic (which is an especially fitting word if the situation is humorous or otherwise amusing).
However, the word is often misused to describe anything that is merely humorous or funny, without the juxtaposition of opposites.
"She was always morbidly afraid of dentists, but then she married one. Isn't that ironic?"
Yes, that's ironic. One would assume that if you are deadly afraid of someone, the last thing in your mind would be to marry him, but the opposite happened, that is, she married a dentist. That's irony.
"She always wanted to marry a doctor, and then she did. Isn't that ironic?"
No, it's not ironic. There are no opposites being compared here. (Yes, this kind of usage does happen.)
"Oh, the irony. I tried to fix a dripping faucet and ended up making such a mess that I had to call a professional plumber and it ended up costing me a kidney."
Yes, that's irony. The attempt was to fix something, but it ended up being more broken than it was, ie. the total opposite result than intended.
"Do you know what's ironic? Your article about tesla coils gave me an idea for a school project."
No, that's not ironic. No opposites happened here. (Yes, this kind of usage does also happen a lot. The example is almost verbatim from something I read, just changing the subjects.)
"The police ordered the robber to freeze, but the robber instead tried to escape. Ironically, he locked himself in a refrigerated room and got bad cold burns."
Yes and no.
There's a funny (or possibly tragicomic) connection between what the police said and what happened then, but that's not dealing with opposites. If the person saying/writing this thinks that the humor in the situation is "ironic", then he is using the word for the wrong purpose.
However, there's another type of juxtaposition here. The expression "freeze" is figurative, and not intended to be taken literally. However, its literal meaning ended up happening. In other words, there's a juxtaposition between taking something literally or not, which forms the irony. Thus in this way the usage of the word "ironic" is correct.
Not knowing which of the two things the original author is referring to, it may be merciful to give him the benefit of the doubt and assume it's the correct usage in this type of writing.
"I find it ironic that you pointed out grammar mistakes in my post but you ended up making grammar mistakes yourself as well."
Also a border case. Technically speaking there are no opposites being juxtaposed here. Person A lectures person B about grammar, and makes grammatical mistakes himself as well. No opposites happening here, so no irony. "Hypocrisy" might be a better word in this case.
On the other hand, some juxtaposition can be seen here in another sense. If someone lectures someone else about grammar, one could assume that he should know what he's talking about, but since he made grammatical mistakes himself, it's clear that he is not as knowledgeable as he pretends. Thus there's a juxtaposition between what this person pretends to be and what he actually is. That could be seen as ironic.
"The irony of writing a good fantasy story is that it must be realistic."
Yes, because it's "fantasy" (containing supernatural and impossible elements) as opposed to "realism" (adhering to everyday natural phenomena and experience), so they can be considered opposites.
"The movie Star Trek: First Contact made a reference to the book Moby Dick, with captain Picard being compared to captain Ahab of the book. Ironically, Patrick Stewart played Ahab two years later in the Disney version of Moby Dick."
No. That might be a curious coincidence, but it's not irony. There are no opposites being involved. (This is another actual example I grabbed from the internet.)
The concept of sarcasm is also related to irony, and also often misused.
Basically, sarcasm means using irony to make fun of someone. or as an insult. In most cases it literally means saying something but meaning the exact opposite.
For example, saying "great job you did there" to someone who failed completely to achieve what he tried to do would be sarcasm.
Saying "you really f***ed up this time" to that person is not sarcasm because there are no opposite meanings involved.
"Yes, keep pressing the button, maybe the elevator will arrive sooner that way" is sarcasm (because what the speaker really means is that pressing the button repeatedly is useless and the other person should stop).
"Pressing the button many times makes you look like a fool" is not sarcasm because there are no opposite meanings involved.
"Don't let the door hit you on your way out." Border case. Could be interpreted as sarcasm in that the literal meaning of the words would imply some kind of concern for the well-being of the person being spoken to, while the actual meaning has nothing to do with that.