I went to Chile, Argentina and Brazil last December. I applied all the visas at their respective consulates in Los Angeles. No big problem with visa application or travelling. But there were irritations.
First you need to have RTD good for at least 6 months after your intended travel dates. Considering it's so unpredictable how soon you can get your RTD after you submit your application, it's hard to time the travel.
I applied for my RTD back at the end of 2003 and I didn't get it until July 2004. When I applied for it I was not even thinking about going to South America.
It took about 5 weeks to get the Brazilian visa. Since U.S. citizens need to get visa also. They are busy.
It only took me a couple of days to get the Argentina one. But waiting for the Chilean visa was killing me. The visa officer told me it'd take about 7 business days. But it took 3 times that long because of the APEC meeting. And the officer didn't know until I started to call him every day and he finally called people in Chile to find out the reason for the delay. It's good that they didn't hold my RTD. So I went to the Chilean and Argentine Consulates the same morning.
I took a flight from LAX to Mexico City. There was about 5 to 10 minutes for them to check out my RTD before Lan Chile attendent let me get on the next flight to Santiago. No hassle whatsoever to get in Chile at the Santiago airport. No problem getting out of Chile at an immigration checkpoint on the mountain bordeing Argentina. But there was delay at the Argentina port of entry. It was a small structure in the mountain sourrounded by big lakes. We arrived by boat. The officer searched on his computer while looking at my RTD for a long time. And he had to check with another guy before he let me in. A couple of minutes later the tour guide called me and told me the officer wanted to see my document again. And again they checked it. Finally our boat to cross another lake came and I got on it and sailed into Argentina. My journey from Argentina to Brazil was delayed for awhile also. I was on this bus going from Iguazu Argentina to Foz de Iguazu in Brazil. The bus ride lasted for within one hour. On border crossing, first everybody got off the bus and went through immigration leaving Argentina. The girl behind the computer couldn't figure out how to process my RTD. Everybody was already back on the bus. Fortunately the driver didn't just drive away with my baggage. He came in the room to check on me again. Finally there was this one guy coming over taught the girl what to put into the computer and I was back on the bus and we left Argentina. Then we stopped at the Brazil check point. This time only me and another family went in to get our document stamped. The officer told me he'd never seen a passport like mine but he let me fill out a form and stamped my RTD and let me in very fast.