In the real world, the RX-78-2 and the other Project V mobile suits were decked out in a Toyetic paint scheme to sell the show to kids. In-universe, they were prototypes, and prototype jet fighters in the 1970s and 80s were painted in similar bright and bold colours. Here's an example.
Why do Zeon mobile suits always have that one red eye? It's a Visual Pun of sorts on how they never seem to win. In Japanese culture daruma dolls are used as a sort of good luck charm to wish for success in an upcoming endeavor, like studying for an exam or running for political office. You paint on one eye when you start and the other when you succeed. The implication is obvious.
By choosing to use colonies instead of the planets, the writers cleverly sidestep the research work needed to make terra-forming seem scientifically plausible.
Mobile Suit Gundam Unicorn reveals that the goal of Side colonies wasn't to colonize the solar system to begin with, but to give Earth time to heal itself.
Whenever Revil puts his flag on a Magellan, the name has a deeper meaning:
At Loum he commanded from the Ananke, meaning "necessity" in Greek. Someone in the Federation sees war as Necessarily Evil... And Revil agrees.
In the counteroffensive his flagship is the Phoebe. In Greek mythology Phoebe is one of the original Titans, grandmother of Artemis (goddess of the Moon and the hunt), Apollo (god of arts, medicine, the Sun, and prophecy), and Hecate (goddess of crossroads and magic), and is herself associated with the moon and prophecy. This should be obvious.
Quite a lot of ink has been spilled to justify why the crew of the White Base reported Char's Zaku going three times faster than the others. Most of the writers forget that there is no such thing as Space Friction and therefore no top speed in space; as long as a vehicle is carrying enough reaction mass, it just needs to keep the thrusters burning to accelerate and it can reach any speed the pilot likes. Char's Zaku doesn't need to have thrusters three times more powerful in order to go three times faster; all it needs is a pilot who's just that skilled and just that reckless.
Somewhat debatable, but Zeon is called a Principality, even though it's lead by a Archduke. The Other Wiki, however, notes that "principality" can denote any society lead by a monarch, no matter what they call themselves. This bothered Fred Schodt, though, and when he translated Tomino's novels he changed the name to "The Zeon Archduchy"; as with all his other changes (Sha for Char, Zak for Zaku, et cetera), it never caught on. The whole thing makes a bit more sense given the nation's backstory. Even after the Zabi family took power and declared themselves royalty, Zeon was still (at least nominally) a semi-autonomous Federation state for a while before they began to push for full independence. Degwin calling himself Archduke instead of King or Emperor was a sop to the Federation's authority. On the other hand, the official English version's more ambiguous "Sovereign" and "Principality" come off as a lot more canny. A principality can, like a duchy, refer to the domain of a noble in a larger empire (as in the principalities of The Roman Empire or the "princely states" of India during The Raj) but it has also been used to refer to small, independent or semi-independent states like those that eventually unified to become Germany and Italy. It's hardly a stretch to think of Degwin, and especially Ghiren, presenting themselves to the Federation as the former while plotting to become the latter.
At first glance Lalah's cheerful appearance seems out of place, considering her past is similar to that of another young lady. But then it's revealed that the Flanagan Institute considered her their star student and she was subjected to testing out Newtype weaponry, and later in Mobile Suit Gundam: Char's Counterattack Char reveals he regrets using Lalah like a machine. Adding this together, it begins to sound very similar to a certain girl in Mobile Suit Zeta Gundam who was a Newtype guinea pig for weapons and subjected to massive amounts of torture and Mind Rape, while displaying an identical cheerful disposition that seemed off. No wonder Lalah seemed happy after she died.
Let's not forget that, before being taken in by the Flanagan institute, Char found Lalah in the streets. Who knows what kind of life she left back then.
According to the manga adaptation Gundam: The Origin, Lalah was working for an abusive man who forced her to use her power to cheat at the roulette and similar things, and was beaten quite often.