The death of Qui-Gon Jinn in the interpretation of Master Skywalker's records receives a nature of self-sacrifice. Having the rare talent of truly becoming one with the Force, Qui-Gon had a vision during the battle, which showed him Darth Maul's real plan, as well as the impossibility of defeating him by usual means.
The reasons for that were the fighters' personal characteristics, as well as the character of the combat training. The ritualized and too showy battle style peculiar to the Jedi, could not stand against the extremely pragmatic style of the Sith, which had the sole purpose of destroying the opponent as quickly as possible. Besides, Darth Maul was superior to his opponents as a Jedi and lightsaber fighter to begin with. Realizing that, Qui-Gon Jinn made the only decision which would have allowed the Jedi to win the battle.
Separating himself from Obi-Wan during the battle on purpose (an action intolerable even for a student under usual circumstances), he, in a carefully calculated (or "suggested by the Force" – depending on the point of view) moment opened himself for Dart Maul's strike. Qui-Gon knew, that being a young zabrak and a Sith (and feeling relatively safe) Maul won't miss a chance to admire his deed.
He didn't. Piercing Qui-Gon Jinn's body with his lightsaber, Dart Maul froze for a moment, looking into the dying Jedi's eyes. That moment was sufficient for Obi-Wan Kenobi to throw his lightsaber and, accelerating it with the Force, to cut through both Maul's forearms. Finishing the Sith after that was a matter of a couple of seconds. That was probably what Obi-Wan meant in his diary. Darth Maul was killed by his lightsaber, but that lightsaber was directed by Qui-Gon Jinn's hand (or, rather, will).
Among further events, there are only doubts about the reconstruction of the talk between Obi-Wan Kenobi and Master Yoda, as well as the fact of Master Yoda's and Master Mace Windu's arrival on Naboo. According to the information available to us (the Jedi Council's archive) Qui-Gon Jinn's cremation took place on Coruscant and went according to the Order's rules.
The scene of the celebration in gungans' honor is shown quite precisely. The deviation from the truth is only in the part of the gungans' uniform and ornaments – actually, they looked much more modest. Amidala's threats towards the Trade Federation, however, are a complete fiction. The government of Naboo couldn't sue the traders officially, since that would have demanded that they uncover all the reasons for the conflict and stop the gugni trade. Considering the necessity of restoring the planet economically after the occupation it would have been very bad for Naboo. As a result, the Naboo government and the Trade Federation signed a peace treaty, the full details of which are still unknown.
And meanwhile, Anakin-Vader did become the padawan of Jedi Knight Obi-Wan Kenobi…