Ren, and later Aichi's repeated statement of "Despair to the powerless, and all glory to the one with the power." throughout Season 1 seems a bit odd, being essentially just a standard Might Makes Right statement. However, it makes perfect sense considerhing who says it. Both Aichi and Ren fell into despair from their own powerlessness (Aichi moreso than Ren) and only reached "glory" through Psyqualia. It's not just an insult for their opponents, it's a reflection on how they got to where they are!
One criticism of the Gold Paladins when they were first released was that they're a Suspiciously Similar Substitute of the Royal Paladins. But when you realise that at least two of their leaders were canonically part of the Royal Paladins (Garmore and Ezel), it makes more sense. Of course they worked similarly to the Royal Paladins, they were trained and led by warriors who are Royal Paladins!
Ren and Kai act very differently from their Season 1 selves during the second season which makes perfect sense considering that they have forgotten Psyqualia and the events surrounding it, which was a core point of their relationship and personality.
In Episode 105-6 Miwa tried to get Aichi to transfer to his school by saying that there is a Vanguard boom in popularity going on in there. He says that, but that doesn't explain why their Vanguard fight club has only four members, even worse than Miyaji.
In season 2, Ren is stated to often lose to Kai despite using psyqualia, and doesn't even try to fight Leon, yet in season 3 he is one of the people Kai looks up to as someone he is failing to catch up with. This is because in season 2 Ren, just like Aichi, is using a Gold Paladin decks which, as above, works very much like Royal Paladins. However, Ren used Shadow Paladins, which had a different fighting style, and were only released at the end of the season. Basically, during season 2 Ren had the flu and could not fight at his best, but once he had his Shadow Paladins back he also went back to be beyond Kai's reach. This is also the reason he keeps trying new decks through the season: he knows Royal Paladins are a bad fit, and is subconsciously looking for his actual deck.
Kai's turn to evil in Season 3 makes more sense when you look at his record in Season 1. He never actually beat Aichi or Ren in Season 1 except in flashbacks. He would have likely lost his fight against Psyqualia Aichi had the fight continued, given the amount of shield Aichi had left, and his attempt to defeat Ren ended with his 'final evolution' being crushed by Phantom Blaster Overlord. In Season 3, he has that as his established record against the two. Why doesn't he try to get stronger by practising more and building up his own strength? Because he tried to do that before, and it didn't work. So when he's fighting Takuto and facing Mind Rape, his faith is already compromised by the fact that his reliance on his own strength hadn't won him the fights that truly mattered. Between the Mind Rape, knowledge that his faith has gotten him nowhere, and the power he's being tempted with, it's small wonder that he gives in.
Towards the end of the 5th Opening, Eradicator, Vowing Saber Dragon "Reverse" and Silver Thorn Dragon Queen, Luquier "Reverse" appear with Star-vader, Infinite Zero Dragon. Why these two in particular? They're the first two Reverse units to be shown in the anime.
And towards the end of the 6th Opening, Eradicator, Vowing Sword Dragon and Silver Thorn Dragon Tamer, Luquier are seen getting shot down and falling back towards Earth.
Suiko's morally questionable actions throughout season 1 make a lot of sense once you consider season 3's reveal regarding her employer Takuto and his method of Recruiting her and the rest of the Ultra Rare and the lengths he went to involving their memories to ensure their assistance. This in turn also explains why Kourin's apparent "spanner in the works" never really goes anywhere as she is in the same situation as Suiko, therefore if she wants her memories returned she must remain a loyal ally until the mission is concluded.
Why Kai is so certain that Ren remember Aichi in Legion Mate. Ren is still his nice self, not his psyqualia-mad self. Since the current Ren is a result of Aichi beating him, and Ren hasn't reverted, he must remember.
The card Star-Vader Blaster Joker. At a glance it looks like just a combination of Blaster Blade and Link Joker, but considering the Tarot meaning of the Joker (the Fool) it takes on a new meaning as the Fool/the Joker represents the "protagonist" of the Arcana.
A bit of Fridge Horror: Myojin's plan is to take away all the luck from Cray and give it to Earth. But the flashback points the beginning of his plan to before the start of season 1. So, if his plan worked, Cray wouldn't have been able to stop The Void... and Earth, now connected to Cray through the Stride Gate, would be it's next target. Do you think Earth's peaceful fortune would be able to stop it from an entirely Reversed Cray?
As Kai puts it at the end of the Link Joker Arc, he tried to shut out his friends in order to acquire strength, signified by Dragonic Overlord "The Re-birth"'s skill to lock all of his rear guards to acquire power. At the end of the Legion Mate Arc, Aichi uses Star-Vader, Blaster Joker to lock his opponent's field and retire their mate. Interpreting this, Aichi is actively trying to push others away, even severing the connection with his closet friend Kai. Ironically, Blaster Joker needs to be in Legion with Photon to do this skill (Kourin's avatar for that season).
Interestingly enough, Blaster Joker's skill can be interpreted as an allegory for the season as a whole. On a full field, the opposing board is locked and the Vanguard's mate is retired, while Blaster Joker's field has four rear guards and a mate with a single locked unit. This mirrors Aichi with Kourin as the mate alongside the four rear guards, the Quarte Knights that oppose Kai, the only one who retained his memories of Aichi at first who had to unlock his friends memories.
For the card game itself
While Grade 4 units are commonplace now a days, a few units are able to become Grade 4 units as Normal Units and not G-Units, they would go on to become G-Units themselves.
Epitome of Knowledge, Silvest has lived for several millennia and is known to train his mind and body thus achieving a level akin to a Grade 4. Appearing once every century or so, he comes to encourage young students but is very illusive thus why his card has an expiration date.
Nubatamas Afterimage: The Nubatama are ninjas. After creating a division (binded opponents card return to hand), the Ninja have enough time to prepare an illusion (afterimage). However they need to act fast to prevent their illusion from being discovered as fake. Since in anime logic, lighter load = more speed (hence requirement of having less than 6 cards in hand).
Nubatama's Dominate: Dominate plays more to their demonic roots rather than their ninjutsu causing a literal Demonic Possession. It makes a bit more sense if you establish them not as dragon ninjas but as yokai spirits utilizing ninjutsu, thus the powers of possession and afterimage would work out as well.
Neo Nectars Bloom: Flowering (bud become bigger due to petals opening up, represented by two unit with the same name), turning a bud into flower (gaining new effect).
Spike Brothers Charge: Spike Brothers are based on American Football, in charging state basically means they are running towards their opponent (to tackle them).
Not just tackling, but recklessly tackling. They get one really good hit in (the big benefits of attacking while charging), then injure themselves so they have to go back on the bench (bottom of the deck).
Link Joker's Lock: They're alien invaders, thus they keep their target in stasis to analyze them and keep them away while preserving their being. After being integrated as a clan of Cray, they also use it on themselves to keep themselves in stasis, to preserve energy and devise a strategy, thus gaining abilities upon unlocking.
By extension, a Reverse unit is given the ability to lock their own allies. In this regard, they are basically absorbing their allies strength to empower their own. Thus why Shadow Paladins and Tachikazes do not have a Reverse unit as they would require a full sacrifice rather than simply stealing their powers.
Deletors Delete: The vanguards attack and ability become blank, basically, you are deleting the text in the ability box as well as their power level in the card.
Delete can also be seen as an evolution of lock: forcibly ejecting the fighter from their vanguard, then locking it so they can't get back in. The same protections that keep a vanguard from getting hurt also protects them from being lock, but deleting overcomes those protections. In doing so, the fighter is left as a defenseless astral body once again, still able to call for reinforcements but only nominally able to fight themselves.
Deletor's Vanish Delete: Basically deleting unit from existence (presumably, permanently).
Tachikazes Engorge: Since Tachikaze are dinosaur... for fridge horror: the reason why rearguards retired is because the said-unit with the said-ability, ate them. Being Engorge state basically means they are satisfied (from eating/retiring the rearguard), hence have the energy/motivated to do other stuff (activating another ability based on how many unit retired/eaten).
Bermuda Triangles Harmony: Bermuda Triangle are idols, harmony is basically an idol group/duet (having two units with harmony ability on same column/stage).
Granblues Hollowed: Japanese Kanji used for the keyword is Apparition and since Granblue are basically undead, retiring at the end of turn after being in hollowed state meaning they are returning back to grave (after returning from it).
Pale Moon's Magia: Stage Magician should come into mind, Magician declared a hat-pulling trick but you dont know what would the magician put out of his empty hat (able to call any unit from soul to rearguard circle) but a magic trick is ultimately still an illusion anyway (return to soul at end turn).
Oracle Think Tanks Oracle: the idea of having more cards in hands(5 or more cards in hand to activate ability) means that they are prepared for their opponent after foreseeing the future.
Nova Grapplers Rush: The japanese Kanji of this keyword is: Fighting Spirit, basically, Rush is a heroic second wind (effect trigger after the Unit with the ability, Stand due to other effect).
Narukamis Thunderstrike: They restrict their opponents movement (binding them) so as to strike them with lightning.
Gear Chronicles Time Leap: They can travel through time. Binding a unit means using the unit to call for reinforcements for a Unit of higher grade from the future (hence from Deck to field).
Why only one Grade higher (chain of command, getting help from their immediate Superior. Having Commanders means Gear Chronicle do have some form of Hierarchy)
Why the Higher Grade Unit return to the bottom of the deck at the end turn?
Because they just went to the past (stuck down there), it will take a while for them to return to the present by taking the long way back. Of course, you can always use time-leap again to get their lazy ass back quickly...
Aquaforce Wave: Aquaforce is a military unit, their multiple attacks probably represent them attacking in waves (new ability after multiple attack because the previous waves are merely to buy time to get another group to come in with better equipment more suited to deal with their enemies.).
Royal Paladin's Brave: Considering that Brave activates when the player has three or less cards in hand, they become more powerful to protect what little reinforcements they have left.
Taking it from another angle, Brave units are going all out knowing full well they may not get reinforcements.
Kagero's Blaze: Fire becomes stronger the more area they cover, translated in the game, the more you have on the field compared to your opponent, the stronger they become.
Gold Paladin's Unite: As sort of the direct opposite of Royal Paladin's Brave, having more reinforcements means they can work together to become stronger.
Angel Feather's Rescue: Medics would rush in to get one of their injured out of danger, but in doing so this would put themselves in danger as well, thus why the Vanguard takes damage.
Dark Irregular's Darkness: Vampires would sustain themselves by constantly drinking the blood of the living, thus why darkness deactivates at the end of turn since it would only sustain themselves for a small time.
Dimension Police's Burst: Superheros constantly push themselves to the limit and upon getting stronger, they may also gain new superpowers. If we apply this to the Dimension Police's Mecha, they unlock more features the more they are powered up.
Megacolony's Dark Device: As an evil organization, they have a means to gain the upper hand when their opponent is down (or in this case rested).
Great Nature's Success: Getting the result they want (in this case the power threshold) means they will have the confidence to move on to the next step (the ability that activates when they become successful).
Murakumo's Shadowstich: By intentionally being blocked, a ninja can plant something worse while they are being distracted by the head-on attack.
Genesis's Revelation: By peering into the future, they can predict what will happen. If that card is sent to the soul, a unit is rested as they just used their energy to change the future.
By extention, Mythical Hellsky Best, Fenrir changes the revelation ability, empowering them so that instead, units can choose one of two possible futures.
Shadow Paladin's Ritual: Occults would believe that they would appease deities or become stronger by sacrificing their own, but not just anyone will do. Thus the skill only counts grade 1's in the drop zone
All of the Zeroth Dragons take some inspiration from the clans of its nation in some fashion when it comes to their skills. Even the exclusion of the G-Zone can be taken as something from any self-retire clan.
Meggido: It firsts calls from Hand or Drop Zone like with Bermuda Triange and Granblue respectively, and the ability to swap units as with Aqua Force.
Drachma: It combines the retire skills from Kagero and Narukami, taken a step further with Narukami as it binds those cards as well. It also forces discard like with Nubatama. The G-Zone exclusion effect can be taken as an extra cost similar to Tachikaze. And while there aren't direct references to Murakumo, Murakumo and Nubatama were once one in the same.
Zoa: It gives the extreme power gain to one rear gard that Neo Nectar and Great Nature are well known for. And while it doesn't paralyze any units, remember that insects, what Megacolony is established as, typically uses toxins or poisons to utilize it's paralyze skills. Taken to its logical extreme, if applyed enough, like say granting one of its rear guards a lot of poison to use, then it will turn it lethal, thus why a successful hit with that unit wins you the game immediately.
Dust: Dusts's primary skill is to remove all of their opponent's abilities and reduce both the Grade and power to 1. This demonstrates the powers of Pale Moon, in which magician can hypnotize their volunteer, Gear Chronicle, regressing time so that they return to a weaker state, and Dark Irregular, with how vampires can take their victim's energy. This leaves the extra damage the opponent takes which can be similar to a blitz in football a la Spike Brothers.
Stark: Stark takes Dimension Police's strong Vanguard abilities and Nova Grappler's multiple attacks and give both of them to the Stark. That being said, it does not possess any abilities of Link Joker, namely their ability to lock, but that makes sense as Link Joker was established as a clan of Cray with the Messiahs late into the lore's timeline (Gear Chronicle is argued to have always been a clan just hidden for a long time).
Ultima: Ultima allows for deck calling in the style of the Paladin clans, deck manipulation akin to Oracle Think Tank and Genesis, and finally strong trigger effects similar to that of the Angel Feathers' rescue mechanic.