None of his actions worked against the sith plot either. Remember that they weren't on the side of the droid army, that was just a bad guy whose presence allowed them to manipulate the senate and jedi and set them up for their takeover/downfall. The first thing Palatine does after he's won is orders Anakin to cut off the head of that bad guy, now that they were no longer needed.

And even though it appeared that the good guys won episode 1, in hindsight I'd call it almost a complete victory for the sith. Palpatine was chancellor, Qui Gon (who might have had the wisdom to help Anakin avoid the dark side) was dead, Anakin (who Palpatine and Plagius caused to come into existence with some force fuckery 8 years prior to ep 1) was in the jedi and was already contentious and being trained by a jedi who was not equipped to handle someone as tempermental as Anakin, and the trade federation was on the radar as a threat to the Republic. The only loss to them was their enforcer, Maul.

The outcome of the battle for Naboo didn't matter to them. Though it was also Anakin that won that battle, despite Jar Jar's chaotic effectiveness for their side. Without Anakin's surprise victory, they didn't really have a path to victory and IIRC they were pretty much surrendering when the droids suddenly went dead, so it wasn't like Jar Jar was even winning the conflict for them.

None of his “accidents” worked against the goals of the heroes and he was always where he needed to be.

Well yeah, he was still in the "gain their trust" phase. The betrayal/reveal was going to happen in the second or third movie.

The whole prequel trilogy was about the corruption of the Jedi and Jar Jar might have been exile or left because of his opposition to it.

Jar Jar causing the corruption of Anakin, more like.

Is it, though?