In The Phantom Menace, a lot of people complained about the submarine having force-field windows. But it's a Gungan submarine. Gungans are amphibious, so for them those windows are a safety feature.
At first, the Jedi Council is dead set against training Anakin, because he is too old, and there are all those Mommy issues... Then, in the end, the Council agrees, though Yoda still is against it. It seems like they agreed because it was Qui-Gon's last wish and they maybe felt that they owed him or something. But that wasn't the reason. At least, it wasn't the only reason. Anakin is the Chosen One (the Council never really doubted that after testing him) who is supposed to bring balance to the Force. That means eradicate the Sith. First, when Qui-Gon tells them about his encounter with Darth Maul on Tatooine and that he thinks Maul is a Sith, Mace Windu is incredulous. The Sith died out, he thinks. Without Sith, they don't need a Chosen One who is a potential loose cannon. But, when Yoda states the Council's decision in the end, he also explains that Darth Maul was indeed a Sith, they are sure of that now. And that is why the Council changed their minds. And, since there will be a second Sith, they will actually need The Chosen One. So he must be trained. It had nothing to do with Qui-Gon dying, but with realizing there actually was a Phantom Menace out there and they could not do without Anakin.
The title The Phantom Menace. It refers not only to the Sith, who are returning unbeknownst to the Jedi, and also to Anakin. Anakin is, or will be, a great threat to the Jedi, but nobody knows it yet.
Darth Maul's double-bladed lightsaber is Awesome, yet Impractical. However, Jedi don't typically swing the lightsaber as one would use a sword. Against soldiers and droids, they seem to swing with little effort. Yet, against another Jedi or Sith, they fall into practical sword fighting and add a great deal of force. Because a lightsaber cuts so easily, the only other weapon that could pose a legitimate threat and pose a fight is another lightsaber. Back to Darth Maul, it's not so much as a double-bladed lightsaber from this standpoint. It's more of a lightsaber staff. His moves are clearly inspired by bo-staff fighting.
There didn't seem to be much reason behind the battle of Naboo (aside from providing action sequences) at first. Once the movies are seen in order, it is much easier to see the subtleties of the ultimate plot and how Palpatine really was manipulating everything from the very start. The Phantom Meance was really a Xanatos Gambit by Palpatine. No matter what happens, he wins. If the Trade Federation successfully invades and takes control of Naboo, he has the necessary sympathy vote to become Supreme Chancellor. If the Queen makes it to Coruscant to plead her case before the Senate, the accusations get that much more dramatic, the Trade Federation's allies have to step in more bluntly to spin the damage, and Palpatine gets a larger sympathy vote. If the Queen returns to Naboo and overcomes the droid army, Palpatine gets sympathy and badass vote. If the Queen returns to Naboo and gets captured by the Trade Federation, he still gets his sympathy vote. Nothing at all the heroes could have done could have changed the outcome to anything but a favorable one for Palpatine. The only thing that could even theoretically have hurt Palpatine is the Jedi capturing Maul and have him testify in a senate hearing as to who his master/employer is.
Panaka staying with the ship on Tatooine. At first glance, this seems like an odd move given that Panaka is a level-headed military-type. And yet, that's exactly why it would be better if he stays behind. Tatooine is a haven for criminals and shady figures — people who don't want to be found. Having Panaka along would make it much more difficult to interact with the populace because his demeanor screams law enforcement, and, given that Qui-Gon's a Jedi Master, any battle skills Panaka would bring to the table wouldn't add all that much more. Instead, an innocuous fool like Jar Jar is much more handy to bring along and this also prevents him from messing with the already damaged ship or accidentally sending a transmission (and thus alerting the Trade Federation of their location.)
Jake Lloyd's Anakin seems too sweet and too nice with no flaws to be a believable character, much less the origin of Vader. However, there is a lot to this kid. The fact that he built a droid is significant. Why? Because he stole the parts. And, bear in mind, Watto's not that bad a slave owner. He treats them respectfully, lets Anakin go home early, and lets Shmi stay at home and not work in the shop. So the fact that Anakin would still want to steal from the guy who, for all intents and purposes, is the only father-figure he has, is telling of his lack of respect for authority, which will became vitally important in leading to his hush-hush relationship/marriage, which will become incredibly important as it drives a wedge between him and all his friends except Palpatine.
On closer observation, he's also shown to be reckless (utilizing a ramp to get ahead in the race, getting involved in the space battle), aggressively confrontational (with Sebulba), manipulative (watch how he convinces his mother to let him pod race by discussing her own lessons about helping people), defiant (to the supremely powerful Jedi Council, no less!), and arrogant (he has no problem talking up his piloting and engineering skills). These qualities seem innocuous in a child, but they wind up being major character flaws for him as an adult.
YMMV on how the viewer feels about Watto, too. At the end of the day, he's still a slave owner actively exploiting a nine year old child as free labor. His slaves are fitted with chips that will explode if they ever try to escape. Shmi finds Anakin's involvement in the pod races terrifying and dangerous, but she has no power to object to Watto using him as a contestant for gambling purposes. The entire reason why Anakin's freed stems from Watto's willingness to literally gamble their lives away. Later in Attack of the Clones, he refers to selling Shmi as "business." Suggesting that slave owner was Anakin's first paternal model holds more disturbing implications than not and may actually lend some insight into the dynamic between Palpatine and Vader.
If you take the time to consider him, Jar Jar may be one of the most selfless and kind-hearted characters in the entire saga. He's saved by Qui-gon, and although he could have merely thanked him and left, Jar Jar informed him that he was honor-bound (despite being banished from his own society and no longer influenced by societal influences) to give Qui-gon a life-debt of service. He then leads Qui-gon and Obi-wan to the Gungan city, despite knowing he'll face capital punishment for returning, and even THANKS Qui-gon for saving his life before Boss Nass enacts capital punishment with glee instead of begging Qui-gon to take him with him away from his fate (and it's because of him helping Qui-gon that he had returned to the Gungan city in the first place). He's then seen going with Qui-gon into Mos Espa, despite not being asked to aid Qui-gon and is often seen trying to help Anakin with his podracer. And when he's both on the ship with Padme and sharing a private moment with the Queen, Jar Jar connects on an emotional level concerning the personal toll of their journey and the affects of the war on ALL of the species on Naboo, and not just speaking from a removed ethical point-of-view or political angle as so many of the other characters are when talking with the Queen. It's important to also note that Jar Jar, true to his word, finally leaves Qui-gon after he dies at the hand of Darth Maul. He may be a bit too buffoonish in a number of scenes (like the battle towards the end), but it's clear to see that he was someone who constantly tried helping where he could, even if he messed up in the process. Not to mention, despite being shocked he's been promoted to general, he's more than willing to go into combat with his fellow Gungans.
The parade music at the end of the film is a jumpy enthusiastic tune in a major chord sung by what sounds like a children's choir. Put it in a minor chord, slow it way down, and replace the kids with a choir of depressed old men, and you get the Emperor's theme in Return of the Jedi. Consider that Palpatine (featured in the Parade sequence) and the Emperor are one and the same, and you begin to wonder how old and in what emotional state the kids in Phantom Menace would be at the time of the Battle of Endor...
"The Queen demands you take her handmaiden with you". Why would Padme risk leaving the safety of the ship to see what Tatooine is like? Because the Jedi Master is going, and he's the best protection for her, especially if the Trade Federation were to trace the ship's location. Better to get the real Queen as far away as possible.
Why would a planet elect a 14 year old Queen? The position is considered sacred, above politics and pure. Best suited for an innocent child.
There are a lot of criticisms towards Jar Jar's character design as a whole, among them being the way the Gungans speak. But one must keep in mind that the Gungans were the native populace of Naboo, and the Galactic Basic would be a new language to them. Their way of speaking is because the Basic was combined with their original Gungan language.
Why does Anakin have an American accent when his mother has a Swedish one and the other person he's always around, Watto, has some kind of Italian/Middle Eastern accent? It's because he listened to the pilots who came into Watto's shop and admired and wanted to be like them. Most of the human ones likely were Corellian (like Han) and have American accents.
The way Qui-Gon and Darth Maul act during their duel while being separated by an energy gate is a summation of the Jedi and Sith philosophies. Qui-Gon closes his eyes, meditates and focuses on summoning the best of his training to improve his skills. Darth Maul paces around, gathering anger and gaining a tunnel vision on his enemy he constantly glares at, focusing on his weak points.
A phantom is like a ghost, a specter that is physically not there... yet it stands before us in spite of that. A hologram is a virtual projector that makes a person appear before an audience as if he's really there despite the fact you cannot touch him for he lacks substances. Save for one scene, and all the scenes that featuring his secret identity, which character only appears as a hologram for the majority of the film?
A mix of Fridge Brilliance and Fridge Humor. When the decoy queen commands Padme (the true queen, mind you) to go clean R2D2, she has this goofy little grin on her face. Why? Because this is a chance to prank her boss, as it were. Padme has her hand maidens do all sorts of crap and now the decoy is able to get a little revenge. "Oh, go clean the filthy droid, Padme. He deserves our thanks, after all!" The decoy knows Padme can't complain so takes the opportunity to get in a little fun. You can actually see the other handmaidens smirking in the background.
One of the biggest complaints about the Phantom Menace is that it is so goofy and kid-friendly; one of the biggest complaints about the Prequels is they don't feel like the Original Trilogy. But that is the point. The original trilogy was a Space Opera and followed that flow. The Prequels are a Greek Tragedy with Oedipus Rex being the main influence. Thus it doesn't follow the same ups and downs of the original because it is working from a different playbook. This also explains why the Phantom Menace is so silly: Greek Tragedies usually start with light-hearted comedy and goofy characters before evolving into dark and tragic stories. The Phantom Menace is merely the goofy 20 minute opening act of a Greek Tragedy.
If people come to this movie knowing nothing about it, they're treated to a small clue as to Padmé's true identity when she says to Qui-Gon, "You assume too much." It's a Meaningful Echo of what Nute Gunray says to Queen Amidala earlier in the film.
In the Expanded Universe, the Empire was notoriously human centric and xenophobic - which makes perfect sense hen you realise that the Empire's founder, Palpatine, grew up on a planet with two different sentient species that were constantly in conflict and distrusted each other.
All the ridiculous outfits that Queen Amidala wears make more sense when you realise that they're to throw everyone in and out of universe off from the slight differences in appearance between Natalie Portman and Kiera Knightley.
Queen Amidala has a decoy so any attempts at assassination would fail. Sounds bad, but it's just something that comes with such a high political position. Then you remember that she was fourteen in the movie, so they would have to hire a similarly aged young girl to take any and all bullets intended for the Queen.
Combine that with little touches like the blasters concealed in the Queen's throne, and the fact that she and her handmaidens are evidently expert shots with them. Just how often do people try to kill these girls?
Realizing that every last character signed their proverbial death certificate in the ending. Anakin gets trained by a grieving, inexperienced Knight barely out of a Padawan braid, who is completely unable to handle the task of an unruly unconventional trainee who hasn't been confined to an enclave all his life. Obi-Wan, said grieving and inexperienced Knight, will be killed by Anakin later. Padme and Anakin have a Precocious Crush that will end in a tragic mess of a marriage and their mutual destruction. Palpatine has been elected Chancellor, starting his rise to power that will eventually destroy almost every other character present, directly or indirectly. Worse, it all looked like a victory at the time.
Even Palpatine sealed his fate there, given that it was Darth Vader who eventually killed him. So, there's that.
C-3PO being built by Anakin means that Luke and Leia kept what was effectively their half-brother as a slave.
Qui-Gon's funeral. They're watching a man they cared about burn. Anakin is even standing on something, to get a better view, as his first proper father figure is slowly being roasted and turned to charcoal.