The evidence that it was the liver, and not the heart is overwhelming. Consider the following sources and quotes from those sources:
According to IMDb, it's the liver. Quote: "The buffalo liver that Wind In His Hair offers to Dunbar after the buffalo hunt is actually made of cranberry Jell-o." From
http://www.imdb.com/title/tt0099348/trivia
According to Movie Mistakes, it's the liver. Quote: "At the close of the buffalo hunt, Wind in his Hair cuts out the liver of the buffalo, holding it in two hands. He stands to take a bite out of it and it's already about half its previous size. When he hands it to John Dunbar, . . ." From
http://www.moviemistakes.com/film319
According to Wiki Answers, it's the liver. Quote: "The liver is very rich in vitamins ect & it would've been considered a choice cut." From
http://wiki.answers.com/Q/What_part_of_the_buffalo_did_John_Dunbar_eat_in_Dances_With_Wolves
According to the majority of replies on Yahoo Answers, it's the liver. Quotes: "Whoever thinks its the heart can just log off, go to the store and rent the movie, FF halfway through the movie, enroll in a biology course, cause you're not gonna be a butcher, though you probably get butchered in sports." " It is definately the liver. Just type in Kevin Costner eats buffalo liver on google and you will get countless sites explaining that scene." "...it WAS the liver." " Liver. It is the richest part of the body including the organs. Lots of protein and when food is scarce, they need protein the most. As a reward, the hunter who made the kill gets the first bite." All quotes from
https://answers.yahoo.com/question/index?qid=20071219185201AAipt0r
According to DS106 (Analyzing Dances With Wolves), it is the liver. Quote: "With the ending part of hunt you see Wind In His Hair offering a piece of raw buffalo meat to Dances with Wolves. That piece of meat is actually the liver of buffalo. In Lakota culture when a warrior is given a raw liver to eat its a sign of respect, a showing that you’re a true warrior." From
http://ds106.us/2012/03/25/analyzing-dances-with-wolves/
And the publications go on and on and on, etc. . . . , vastly outweighing those few people who state it was the heart.
I think it's safe to say that it was the liver he ate and not the heart.