First of all, it's important to remember or realize that Schindler's List is not a documentary, nor is it a docudrama (a retelling of actual events). It was based on a novel of historical fiction by Thomas Keneally, so the best you can say of the movie is that it is based on actual events in history, even if Spielberg had his own team of researchers.

It would take something of huge length to thoroughly break down all of the movie’s details and discuss which are fact or fiction and why. Also, that has been done many times, so there’s no point reinventing the wheel just for this sub. I don’t know all the answers for all the details, but I’ll talk about some things I do know about.

As many critics and detractors have pointed out, the movie absolutely can’t be seen as anything close to a full representation of the Holocaust, because the movie is a relatively simple story (with a Hollywood structure and Hollywood ending), mainly about two men and the 1,300+ people that one of them helps to save. While the Holocaust is a much larger thing, about cultures and governments and countries with many millions of lives and deaths involved.

There are some things in the movie / book that are included as symbols for ideas or changes because we don’t have accurate and detailed information to pass on, or because a movie has combined / edited / cut things for dramatic effect / time constraints. One example is the girl in the red coat. After watching the movie, one thing I (and some critics) had a problem with is Schindler’s character and (lack of) motivations. Schindler was initially sleeping with the enemy, literally and metaphorically, and then suddenly he makes an abrupt turn and decides to risk his life to save as many people as he can. In reality, Schindler didn't really say much about why he did what he did or why his focus changed, other than that it was basically the right thing to do. But in order to bridge the gap in his character arc between carefree playboy and passionate savior, the book / movie had so show some kind of spark or catalyst.

In the book / movie, Schindler is with his mistress, Ingrid, and he looks out from Lasota Hill, across Plac Zgody, and sees Nazis shooting people point blank, and rounding up others to send off. He sees an innocent girl in red witnessing these horrible things with the Nazis not at all hiding their actions from her. But did this really happen? Kind of, but not exactly. These things are a combination of stories and fabrication of others. The book gives a specific date (June 9, 1942), but the sequence of events depicted on that specific day in the book / movie do not exactly match what historical sources tell us about June 8-10, 1942.

Also, in the book, that little girl in red was named Genia, who was at first hidden by a German family. On the day of these events the family was afraid the Nazis would find her and punish them for hiding her, so she had to leave. She was found and taken to the Plac Zgody roundup, where Schindler was watching from the hill. Again, these are the events in the book.

In reality, there really was a girl named Genia, whose aunt and uncle told Keneally about. The stories that her family told Keneally are the reason she was included in the book. She did like to wear a red cap, and she was rounded up in June of 1942. But she was found and taken near the Optima factory, not at Plac Zgody, so Schindler couldn’t have seen her from the hill. And anyway, Schindler was probably not even on the hill during that week. Schindler was at that hill in March of 1943 where he witnessed Jews being ripped out of houses, so the two stories were probably just combined into one. Also, his mistress was not named Ingrid, it was Marta / Eva, and he probably had another mistress at the time with deeper implications concerning political connections. (Crowe 203-206)

One powerful scene from the movie is when the women and children are stripped and then forced into a large shower room. Many of us in the audience know that people were killed in gas chambers that were disguised as showers. So there’s this tension we feel and you can see in the women’s eyes the fear they have. And just as panic starts to set in the water comes on and the women are relieved because they’re safe. But this scene didn’t happen in real life. The scene implies that at least some of the women thought they were about to be killed by gas, which is what the audience is worried about. But they couldn’t have had this feeling. They had just arrived at the camp and very few people at that time knew about any mass-scale deaths in the concentration camps, let alone deaths in gas chambers disguised as showers. Here’s one short correction letter by a survivor on the subject: http://www.nytimes.com/1994/02/25/opinion/l-schindler-s-list-errs-on-gas-chambers-299499.html

There are also deeper issues surrounding the myth of Schindler that have come out since the movie’s debut. One example is that the movie gives the impression that Schindler wrote the list and frantically added more and more names at the end to try to save just a few more people. Crowe says first of all that there were different lists of various authors, but that "Schindler had almost nothing to do with the list".

Mr. Crowe said that there were nine lists. The first four were drawn up primarily by Marcel Goldberg, a corrupt Jewish security police officer and assistant to an SS officer in charge of transporting Jews. (Goldberg was later accused of accepting bribes and of favoritism.) Schindler suggested a few names, Mr. Crowe said, but did not know most of the people on the lists. The authors of the other five lists are unknown.

Mr. Crowe said the legend of "the list" arose partly from Schindler himself, to embellish his heroism. He was trying to win reparations for his wartime losses, and Yad Vashem, the Jewish Holocaust memorial organization in Jerusalem, was considering naming him a "righteous gentile," an honor given to someone who risked death to save Jews. http://www.nytimes.com/2004/11/24/books/24schi.html?_r=0

So some of the movie and book were dramatized to varying degrees for various reason. This is partly why some survivors, and reviewers have called it anything from kitsch to “astoundingly stupid”.

In the end, it’s a movie that created a LOT of helpful discussion about the Holocaust and recorded video interviews with hundreds of survivors to create a permanent, first-hand record of the Holocaust. So I think we can forgive Spielberg for making a less than true-to-life drama.

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Crowe, David. Oskar Schindler: The Untold Account of His Life, Wartime Activities, and the True Story Behind the List. 2004.

edit: wrong name for mistress

This is a bit different from rkiga's answer but it had to go for less accuracy intentionally.

Amon Goeth, according to Spielberg, had to be significantly toned down for the film. To actually include everything Goeth did while commandant at the camp would have been cartoonishly evil. So they had to tone down his evil to make his character more believable.

In real life he personally murdered people daily, had dogs trained to kill prisoners on command, beat his maids, had entire work details murdered if one person escaped, and shot people from his balcony. During the liquidation of one of the ghettos he personally went around to murder women and children. Very little of what he actually did is portrayed in the film.

One source of interest is the book, "Searching for Schindler", written by Thomas Keneally (the author of "Schindlers Ark" on which the film was based) in which he records how he first came to hear of Oskar Schindler (in a briefcase shop in Los Angeles !) and subsequently travelled to Eastern Europe to meet people who had known Oskar Schindler and who had themselves been on "the list".