The first thing that should be understood about the phrase politically incorrect is that it is what the philosophers call an indexical, a word whose meaning cannot be determined without knowing the context in which it was uttered. Obvious examples are words such as I, here, and now. A less obvious one is promiscuous, which means "more sexual variety than..."
At that point, it's what the mathematicians call an open sentence. (I told you I like the New Math.) We can't tell if the statement is true until we know, more than what? That depends. For some people, it is simply "more than I would." Others would be willing to concede that their own behavior is not the benchmark, and would set a numerical value: more than one in the same day, more than one in the same lifetime, or somewhere in between. Still others would know it when they see it. My own suggestion would be the reflexive definition: more than the individual is happy with.
Obscene is likewise an indexical. As Robert Anton Wilson has pointed out, if obscenity were an objective property, it would be possible in principle to devise an obscenometer that could be pointed at a book and would give a reading in smuts or mackinnons. Likewise, some people's definition of drug is "any mind- or mood-altering substance I do not use."
Politically incorrect is an indexical. It seems to be most typically used to mean, "I want to say this, but They won't let me." We have to know who is speaking, whom the speaker means by They, and what They are doing to prevent him.
It is most likely to be used to refer to pressure coming from what is perceived as the Left, enforced by moral suasion, lawsuits, and—in the case of universities, but not otherwise—firing. A doctor prohibited by federal law from mentioning abortion to a rape victim (what loaded rhetoric?) usually does not say that such a reference would be politically incorrect. Burning a flag (USA, rather than CSA) is likewise not called PI. For that matter, I have frequently heard anti-PC rants from people who get really nasty if you say "Civil War" instead of "War between the States."
Another philosophical term: "Politically," when it precedes "correct" or "incorrect" is an alienans adverb. It casts doubt upon what it modifies, like so-called or self-styled or perhaps more precisely, like statutory, as applied to rape, in that rather than flatly denying the applicability of the term, it suggests that the term is being modified and extended.
Most people say they want to be right, rather than correct. It is linguistic coincidence that the words correct and rectum sound alike, but those who place most emphasis on correctness tend also to be those who fear that they will be inundated by a black tide of mud if they do not maintain tight control.
I don't find the "PC problem" as bad as some say. It's been said that "PC" stands for "plain courtesy," and indeed PC at least started as an answer to a whole lot of really stupid and offensive things that have been said about Blacks, women, gays, etc. When the PC wars started, some otherwise intelligent people began proudly announcing how politically incorrect they were. I would never boast of my abilities in an area where David Duke can excel without even trying.
And often the rules don't seem terribly onerous. It doesn't seem all that difficult to say, "firefighter." And yet I complained about recycling a while back. This probably means that I'd rather pay attention to my words than to my garbage. [I will take it even further: I like Political Correctness. I like being able to work for the general good by using verbal precision and cleverness. Patrick Nielsen Hayden has pointed out that there are Leftists who are more concerned with verbal forms than substantive issues. This may be one reason.]
The paradigmatic case of PI is something not harmful per se that one refrains from saying for public, political, environmental reasons. ("What if everybody did it?") If I tell a joke about a dumb black person, I am not doing immediate harm, but I am polluting the noosphere. I am helping to encourage nasty, erroneous beliefs about blacks.
I will generally avoid antiblack jokes, or try to defang them or distance myself from them. What I find oppressive is the Political Incorrectness of jokes about dumb white people, or of any indication that some people are dumber than others. (It's worse to tell jokes about "polacks," as if Polish ancestry were a sign of stupidity; than about prolacks: members of the working class stupid enough to belong there.)
Likewise for jokes about crazy people. When I first heard that there was a group called Stigma Busters, trying to stop mockery of the mentally ill, I said, "How many Stigma Busters does it take to suppress a joke? One to write a forceful letter condemning the joke and then be afraid to go out and mail it, one to blame the joke on the mind-reading radio the Jews inserted in his neckbone, two to argue over what the body they share should do about it, one to abblabuggugleblub…"
I'll tell you how bad it is. That kind of PC enforcement actually made me sympathize with the XFL. I don't know if the Xcremental Football League really was the trashiest enterprise in all the history of all sports, as some writers have suggested, but it was certainly Top 5 material. It was minor-league football (at a time when there's a noticeable dilution of talent in the major league), tricked out with the TV versions of sex and violence, which is to say, cheerleaders in pandering costumes, and an attempt to pretend that the game is more dangerous than it is. The only thing that kept it from the bone-deep meretriciousness of Temptation Island was that the producers couldn't figure out how to script it. But when a group of would-be Political Correctors complained about the offense to the mentally ill in calling a team the Memphis Maniax, I decided that I supported the league in this matter. (But not enough to watch it. There are some sacrifices I will not make, even for civil liberties.)
There are of course other forms of incorrectness. I've often thought there could be money in The Psychologically Incorrect Book, with chapters like "Who Says You Have to Be Assertive?" "Codependence, the Friendly Way," and "Denial: Your Road to Peace of Mind." As with political correctness, psychological correctness is enforced by opinion, rather than law. Mind-body dualism is ontological incorrectness.