At the end of Yakuza 1, the Kazuma and Nishiki fight and one has a carp tattoo and the other has a dragon tattoo. Well, there's a legend of a certain waterfall that if a carp manages to swim up the waterfall, he turns into a dragon. They both started in the same place (the orphanage/bottom of the yakuza) but only one of them was able to make the journey to become a dragon.
At the end of the fourth game, Akiyama allows pretty much his entire fortune to be blown into the wind. That's an insane amount of money and seems incredibly dumb. But it makes sense for a couple reasons:
He had repeatedly said that he's "betting it all on Arai." Arai not making it to the top means he lost the bet, so he feels like he shouldn't have the money anyway.
Consider how he got his second chance in the first place: finding money blown off the tower during the ten billion yen incident. Stands to reason Akiyama, who is all about helping people in need, would want to give someone else the exact chance that he got himself. Times ten.
Another possible reason, slightly more simple: he just doesn't care. From his habits at Sky Finance, and his reactions to his money being stolen, indicate that he doesn't care about the money, as he has so much already, and is in a situation to easily make more. Being so rich as he is, he's lost all sight of the value of money.
It's pretty clearly spelled out in 5, but "Sky Finance" is a reference to how Akiyama first got his money... from money falling from the sky.
The various fighting styles Kiryu has in 0 and Kiwami are slightly off-putting considering how they don't make any canonical appearances from those games onward. However, you can look at his Legend style as the culmination of the three styles he's used in those two games - the speed of Rush, a much more refined technique used in Brawler, and the power-oriented and weapon-based moves of Beast are all present with the Dragon of Dojima style. A similar comparison can be made with Majima's Mad Dog of Shimano style as well - Thug represents his underhanded way of fighting in general, Slugger represents his use of weapons and Breaker represents the blinding speed at which he attacks and his unpredictability.
Terada ended up getting his revenge throughout the years as many believed the reveal that Terada was actually a Korean. After Nishiki killed Sohei to protect Yumi, Terada finally saw that Nishiki indirectly avenged him and helped him find the missing yen to get back at Kazama. Then when Shimano attempts to kill Kazama and Haruka with the grenade, Terada is slow enough to let Shimano kill Kazama and finally avenge the death of his comrades. This also explains why he doesn't go through with the plan to actually destroy the Millenium tower, as the sole survivor of the Massacre at the point, he had already long avenged the deaths of his comrades and only commit only so the cycle of revenge dies with him.
If one thinks about it, Tsuneo Iwami is a fitting final boss for Kiryu, despite his mediocrity compared to, say, Shibusawa or Mine, two comparable ambitious antagonists, because he acts as a twisted reflection of the Dragon. Both men went against their fathers' wishes to join the underworld, building their way to the top. However, while Kiryu made his way up through his own two hands, Tsuneo schemed and backstabbed everyone he could while leaving the dirty work to his men, in order to take the title of Takeru Kurusu. Whereas Kiryu has nothing but respect for Kazama, his foster father, for raising him the way he did, Tsuneo resented his father for preventing him from heading the Yomei, having nothing but contempt for him as a result. It's no wonder Kiryu ends up thinking very little of him, daring to call Tsuneo "Little Baby Iwami", and stating in the fight's objective that he meant nothing to him.
From a gameplay standpoint, not being able to call Omelette at night as a Poundmate in Like a Dragon makes perfect sense since hens in real life aren't exactly the most nocturnal mammals and they usually lay their eggs at the crack of dawn.
There's also some Fridge Humor to be had in the fact that, if Zhao is in your immediate party, Kiryu will attack (and thus down) him a lot. Maybe he was probably reminded of Lau Ka Long and especially Ed when he sees Zhao? Completely understandable given Zhao's Cool Shades are pretty similar to those of Ed's.
The Post-Final Boss of Like a Dragon, Ryo Aoki/Masato Arakawa being very easy is, like the above, another excellent case of Gameplay and Story Integration. Masato had been bound to a wheelchair for a majority of his life, requiring surgery in the United States to be able to walk again. And even when he could walk, he's spent a majority of his time scheming and ordering other people to do his dirty work, usually killing them once they've served their purpose, nevermind being a politician first and foremost. Ichiban on the other hand, was a former Yakuza who, even as a teenager, got into fights a lot and survived the same conditions as an infant that would put Masato in a wheelchair. He also survived getting shot by Arakawa and getting dumped in the garbage for three days without dying from blood loss. Nanba even said Ichiban partly survived because he was so tough (and lucky, of course.) Is it any wonder why the final fight between the two is essentially a Curb-Stomp Battle on Ichiban's end?
Masato's murder at the hands of Kume was bad enough, but the worse part about it is that it is unlikely Kume was unlikely to face justice for what he has done as Masato had been known to be a firebrand in the political arena who did not hesistate to blackmail his fellow politicians to get what he wants and relied heavily on Horiuchi and his associates to cover his misdeeds. Kume actually made himself would have made himself useful by accident by making a majority of Masato's secrets went to the grave for Horiuchi who would have made sure Masato couldn't testify against him.