I was surprised I haven't weighed in on this one yet
I have to agree with MattiasB on names like "gordo" and "negro" (and their various forms). It took me a bit by surprise to hear people calling each other this at first, but it's true, completely names of endearment. One of my sister-in-law's best friends is quite morocha, an Argentina, and everyone calls her "Negra." In fact, that was the actual nickname given to her at last week's high school graduation ceremony in front of the whole school. No one thinks twice about it having any negative connotations. And yet so many people here want to be fair-skinned with blue eyes and blond hair...
However, "Paragua" (umbrella) is not a term of endearment, to the Paraguayans I know. Being married into a large Paraguayan family, a large portion of which now lives in Buenos Aires (not just direct family but cousins, uncles, etc), I know for certain they take offense to that particular exp<b></b>ression.
Both my sisters-in-law who attend high school here have been called "Paraguaya Sucia" by a goodly portion of their classmates. "No es por mal, solo te estamos cargando" (we don't mean anything by it, we're just kidding). My older sister-in-law tried to date a few of her classmates until she realized they wouldn't talk to her in school at all and acted like they barely knew her when she approached, only by phone of Facebook after school. Some of her friends told her it's because they assumed she would "put out" because she's Paraguayan but they didn't want their friends to know they were seeing her, being a Paraguayan. And she doesn't "put out", so those "dates" never lasted long. She was the only one that only had a few clapping for her at her graduation ceremony last week (her family and her close friends), as opposed to everyone else getting practically standing ovations from everyone there.
She dated an Argentine older boy not too long ago (she was 17, he was 20) for a couple of months. His father was supposedly the president of a large Polo organization (now deceased). They live over near us in a very posh section of town. He was terrified to bring her to meet his mother - he told me about her attitude regarding Paraguayans and other "low class" people (although he told my sister-in-law that his mother would love her - but they never quite seemed to meet...). When she broke up with him (he wanted to move in with us and although he denied he wanted to marry her, he was so clingy that it was obvious what he wanted), he heaped all kinds of name-calling upon her (some of it from the street below our apartment as he alternatively called her ungodly names and tried to get her to take him back at the same time). I'm sure it would have made his mother quite proud.
She is now dating a boy a year younger than her, who seems like a very nice young man. His parents seem like good folk, as well.
When we lived out in Garin (about 12 klicks toward the city from Pilar, in a closed neighborhood - we left to come back to the city about 4 years ago), she attended a school out there that was quite different. The people out there in her school (the more "common folk", that is) treated her quite well.
However, my wife was shunned in our neighborhood. The only friends she could make out there were with the maids (almost exclusively Paraguayan). The maid next door repeated what her "patrona" had to say about us - apparently the patrona and her friends talked amongst each other with no regard whatsoever as to who might overhear her (i.e., the Paraguayan maid). Let's say it wasn't flattering, both as an American and as a Paraguayan.
I have been directly discriminated against as an American, though not very often. I was once in a cafe with four of my expat friends. We were at one table speaking in English and the guy at a nearby table took umbrage with this, for some reason. He was a rugby player with his girlfriend. At first we thought he was being friendly and making some joking comments, until he started to become very rude and told us directly that we have no business being here and speaking our vulgar language. He made a number of other seriously disparaging comments and got verbally belligerent until I stood, he stood, and I offered to meet him outside, at which point he went back to his table, paid the bill and left with his girlfriend.
Another time a few of us took my car out to Matadero to get some meat at a carniceria I know out there and we had to wait a long time (very popular place). We decided to go grab a pizza at a local restaurant. The three of us sat there and waited for our order to be taken for almost half an hour. Meanwhile, we saw a number of people get seated and orders taken, and even served. No one ever came over to take our order, or even bring bread to the table. We gestured to the waiters a number of times - they either never looked at us, or looked away when they saw us beckoning. We got up and left and went to eat at McDonalds.
For me, as an American, I have found very little discrimination, really. It has happened, but no more than i would expect just about anywhere in the world. I do find that I make friends far easier among the "working class" rather than the richer folk. I have a number of friends who are "moneyed" and find exactly the opposite - many of their friends are from the upper stratus of Argentine culture. Some of them are as prejudiced as their Argentine friends.
For my family, as Paraguayans, they find real discrimination, often.
Of course, the Paraguayans call Argentinos "kurepi" (Guarani for "pig skin"). I wouldn't say they are without prejudice either. Theirs (according to them) comes from the War of the Triple Alliance (1865-1870), where they feel like Argentina (and Uruguay) stabbed them in the back by siding with Brasil in the war. Apparently they have long memories...
My overall experience here is that the "upper class" of Argentina (at least porteños, and at least the older generation) are quite prejudiced. Hard to say racism because they are all Latinos mixed with indigenous blood and that of European (my wife's family on her mother's side came from Spain some 100 years ago and there are MANY German-descended Mennonites who live in their area in Paraguay). Although I think a lot of upper class Argentinos, even morochos, think of themselves as European. My portero is from Entre Rios, apparently from a fairly well-to-do German family there. He's been the portero in our building since 1972 and he still speaks Spanish with a recognizable German accent. He's actually quite prejudiced against Argentinos in general, from a distinctly German point of view.
What gets me is when I hear how "unprejudiced" Argentinos are, from Argentinos themselves, while saying how absolutely terribly racist are Americans. I'd say there is a probable equal mix of prejudiced folk both here and in the States, but here it seems it is hardly acknowledged, and yet is more in the open and even accepted to an extent.
Personally, I don't particularly care for "political correctness." I understand the desire for everyone to treat everyone else correctly (even if you have some prejudices), but some times it is taken too far. In the States it is, in my opinion. It doesn't really hide anything; however it may be a cause for change over a longer period of time, and for that I do applaud it - but it does sometimes become oppressive.
Here, there seems to be very little political correctness, but a lot of people don't seem to even realize their prejudices.