Rational is used wrong about 99% of times. People will say something is irrational because for instance they will have some math equation that they will say about that they will say things are irrational. The problem is that their equation is wrong and even worse the equation is usually the least wrong thing they are wrong about about everything.
Yeah, I find that people use "Logical" wrong as well, or, more specifically, "Not Logical" or "Illogical". When asked to explain why something is or isn't logical...blank stares.
Once, a couple of years ago, I had a chat with a woman online, and I used "rational" in describing a given choice (we both disapproved) - something like: "Well, this is not something I consider rational".
She was a bit surprised at my choice of words (we were basically in agreement on the main topic, but the moment I said "Rational" she reacted badly) because in her experience "rational" is almost a bad word, because (according to her) it is banded around (by men) to belittle their counterpart in a discussion.
I told her that I had just finished an online course on IA, and therefore I meant "rational" strictly in the sense of "rational agent" as per Wikipedia: a rational agent is an agent that has clear preferences ... and always chooses to perform the action with the optimal expected outcome for itself from among all feasible actions.