The current Star Wars mania gives me Star Wars on the mind which reminds me that "Episode 1" sucked. As a shitty fanfic writer, I will ask the question: what could be changed to make the movie better? Let's skip the popular opinion of cutting Jar Jar and consider other possibilities.
Anakin is older and tougher
The young Anakin was too cute for the part of a slave mechanic daredevil who gets the hots for a sexy princess. He ought to be a teenager of around thirteen or fourteen years old. This is still young enough to be considered a kid but old enough to get greasy and sweaty working on his racing pod in the sun, to be a bit surly and rebellious, to be too old to join the Jedi, to have some PTSD from being a slave, etc.
Change the explanation. They do not contribute to the Force but are naturally attracted to those who are attuned to it. Then again, there could be debate within the Jedi on this issue. Qui Gon might be among those who mistake correlation for causation, and this could result in the exact same dialogue in the movie. In any case, the canon will be that the Force does not have a known cause, it simply is.
Anakin loses the pod race
Anakin's pod is damaged or sabotaged and he comes in second or third behind someone else who plays no other part in the story. The Jedi return to Watto's to hand over the ship they gambled on the race while trying to come up with a last minute plan. Watto has a representative of the Trade Federation on screen to witness the transaction, presenting an example of the Federation's influence in the universe.
To the Jedis' pleasant surprise, Watto allows the Jedi to leave with the boy in exchange for the promise of their ship or credits of equal value by the end of the year. "You saw that he has talent, and I was having him sweep sand off the floor. Anybody can do that." Watto is in a good mood. He bet on the guy who won.
This change changes the characters. Watto is shown to be more humane than the audience expected, which makes him more believable. He is still making a profit out of the deal. Anakin is no longer a miracle boy, and the loss gives him the opportunity to express dark feelings towards whoever he blames for it.
An elected monarch. Pfft! HA HA HA! Seriously?
Amidala's status was one of the biggest clunks in the story and needs to be fixed, so let's fix it.
Amidala is not a queen as we know it but more of a beauty queen. Her power is limited to resolving issues that the advisory council is unable to agree on, granting pardons, and being a walking symbol of prosperity. One of her duties might be to select a great work of artistry, industry, or engineering from proposals given to the council by the public, with this project becoming a focus of public pride.
There may be a scene where the queen is walking down a hall with a prospective candidate for the next queen election. The candidate expresses her concerns about Senator Palpatine who is very persuasive in person but there are inconsistencies in his written words.
So the Jedi arrive asking to speak to the Queen that their computers say is the planet's leader. The locals laugh at them and explain that the advisory council holds all of the power.
Jar Jar's people are the Naboo natives
The humans of Naboo are Coruscanti in origin, likely after a hop or two from another colony. There are hints of imperialism in how they manage the planet.
Jar Jar's people call themselves Naboo, a fact learned late in the movie when the Jedi meet with them. The Coruscanti (humans) call them Swamp People. The Trade Federation gives them no respect whatsoever because they do not have space flight.
The Nabooans in the human settlements are mostly diplomats or traders. They might only be in the background of the movie but they are high class and respected by the humans as individuals even if the humans don't think much of their race as a people.
The ending starfight
There is too much Spielberg and not enough Star Wars in the ending starfight. That should change.
The older, tougher Anakin steals a starfighter because he wants to get into the fight. The pilots' chatter with him is a mix of "don't get yourself killed" and "we're too busy to babysit you."
Anakin concentrates too hard on the fighter in front of him to notice a fighter on his tail. R2 bleeps, but Anakin wants the kill. Something happens to knock down the fighter following them, either a Nabooan pilot takes it out or R2 disables it by transmitting a shutdown code. This foreshadows Vader getting hit from behind in the original Star Wars.
Whatever destroys the Federation ships is not an innocent mistake but an organized attack with a battle plan.
The Nabooans would have to transmit a shutdown code from a command ship and prevent the Federation from overriding the code. They need the shutdown code (possibly obtained when the Jedi were on the Federation ship). They need to shoot their way onto the ship, land, and fight through defenses to get to a terminal where they can send the code. Then they need to do something to ensure that the code reaches all Federation drone forces on the ground and they need to do something to prevent any other Federation officers from overriding the code. The Federation may not have all of their eggs in one basket with only one command ship.
There are only a small number of Federation officers per capital ship because they rely on drones to man the ships. The trade federation officers escape on an unarmed shuttle. As they escape, the Nabooan pilots receive casualty counts from the ground, curse the federation, wish that the shuttle crashes, etc. Anakin shoots down the escape pod because he's Darth Vader.
Nabooan pilot: "Pilot, let me remind you that it is against universal combat regulations to fire on an unarmed craft. I will need to give you a verbal reprimand when we return to base."
Anakin: "I am not in your chain of command."
Nabooan: "Very well then. All units prepare to scan the area for ejected pilots. We will form a grid pattern..."
Second thoughts about Anakin
Qui Gon Jin starts to get second thoughts about Anakin but he is killed by Darth Maul before he can express his concerns to Obi Wan Kenobi. Obi Wan carries on training the boy, despite his own second thoughts, because of his trust for Qui Gon Jin.
Finally, about Jar Jar...
Let me explain why the Darth Jar Jar theory took off. They tried to make Jar Jar a lovably silly comic relief character and instead made him unbelievable. They overdid it so badly that Jar Jar's character is better explained by him being a secret Sith Lord than by the story that the movie presents to us.
So let's roll with it. Jar Jar is now Palpatine's apprentice on Naboo, a Sith in training. However, he is such an incompetent fuckwit, or his position is not worth exposing through action, that Palpatine calls in his other apprentice Darth Maul to handle the Jedi. What about the rule of two? Palpatine figures that it is safe to have an apprentice on different planets like a sailor might have a girl in different ports, and he has no fear of Maul and Jar Jar ever getting along well enough to threaten him.
Palpatine has told Jar Jar that there are other Sith out there and they are competitors, threats, not allies. Jar Jar does not know that Maul is working for Palpatine.
When Jar Jar was rescued by the Jedi, maybe he had put himself there to be rescued by the Jedi so he could spy on them.
Jar Jar might be recognized in the palace as someone who they have seen around before, as a friend of Palpatine. The native Nabooans do not trust him because he was practicing amateur Dark Side techniques on them and got caught.
Jar Jar maintains plausible deniability. He reports to Palpatine about what the Jedi are doing, but to the audience they are just talking. He knows that Maul is a threat, but to the audience Maul is obviously scary. By the end of the remake we have dropped several hints of Jar Jar being a Sith but we leave the question open enough to scrap the idea in the remakes of 2 and 3.