The battle between Qui-Gon and the Sith-zabrak Darth Maul on Tatooine indeed took place and went quite close to what was shown in the movie. Another thing which was shown all but completely true is the events on Coruscant, including Palpatine's elections. Parts of these scenes are actually documentary material from the Senate's archives which was but minimally adjusted (it's a sight for the sore eyes on the background of inaccuracies and conjectures).
Discussing the conflict in the Senate is also most interesting from the point of view of analyzing Palpatine-Sidious' political talent. Watching the TF having to defend against a false accusation of occupying Naboo because of disputes in taxing politics without having any worthy arguments to present in its own defense and without any possibility to reveal the truth about the conflict (the reaction on TF's participation in illegal drug dealing would have been most negative and devastating.) can be for a source of great intellectual pleasure for a politics researching historian.
Unfortunately, we know absolutely nothing about how close to the reality the movie shows the meeting of the Jedi Council where it was decided that teaching Anakin might be too dangerous. At least, the historians haven't got a single reliable document describing the course of that meeting (which is most unusual, considering the manic accuracy of the Order's record keepers). Neither is it described in Master Yoda's memoirs, although he does mention that such a meeting took place. As a result, the film is practically reconstructing the respective part of Obi-Wan Kenobi's memoirs – and whether or not they are precise historically is very much doubted nowadays.
Amidala's departing for Naboo is shown with certain pieces cut away. For example, the movie doesn't mention the so called "A-Legion" which consisted of volunteers from the depths of Coruscant and according to Amidala's and Palpatine's plans was supposed to form the core of the guerilla army. The "Legion's" dispatch to Naboo was delayed by Palpatine under the pretense of checking and training the people, and then cancelled altogether after receiving the news about the liberation of Naboo.