Awesome Music: A wealth of examples within the anime:
[https://www.youtube.com/watch?v=_1x0cGFy07U[ Ai Yo Kienaide]], the anime's first opening theme, definitely qualifies. It's well sung with a catchy tune that also captures the sweeping feel of Tokyo's vista and Ryo and Kaori's reliance on one another, all while encapsulating The '80s perfectly.
The singer Kahoru Kohiruuimaki released a version in 2014 with more instrumentals, that sounds absolutely stunning. It can be heard here.
[https://www.youtube.com/watch?v=wK3_ZhGpKsQ[ Get Wild]], the ending theme for the anime's first season, is also an amazing number, which fostered the best animefade-in ever. Don't deny it — it really is. It's a rare example where, while most anime change their endings more than their openings, this one lasted the full first season, that's just how much awesome it is.
Give Me Your Love Tonight, the first insert song used in the anime, is also a winner, with a funky tone, fizzing synthesizer leads which encapsulate the sweeping urban grittiness of 80s Tokyo and a killer beat.
Mr. Private Eye stands among the best of the anime's insert songs, with beautifully-sung and effective lyrics, a silky, sweeping melody and a memorable instrumental backing.
Without You is an engaging pop-style romantic number that sums up Kaori's feelings towards Ryo.
Otherwise, the opening theme of The Secret Service, is a hard-hitting rock number perfectly fitting the series.
Broken Base: Fans often debate whether or not the manga/anime was superior in its earlier incarnation (where it was a Darker and Edgier action series with less mokkori and more realism) or after Kaori began to use her 100-ton hammer (where it became a Lighter and Softer and more comedic series, albeit with the increased character development of the recurring cast (particularly Umibozu) and Ryo's and Kaori's growing relationship earning some popularity with fans).
Ryo began to become a victim of this as the series progressed, becoming goofier, more incompetent when not faced with a life-or-death situation (which, let's face it, isn't often for Ryo) and essentially using his comedic mokkori antics to make girls feel better about their situations (this is actually implied in a few earlier episodes, but it isn't one of the main benefits he provides to his clients as is later indicated).
Umibozu is also hit with this to an extent, gradually decaying from a stoic, threatening and highly competent hitman to a sensitive comedic figure by the end of the anime. Toned down in the manga, however, and while Umibozu's decay is worsened in the anime, he's still perfectly able to segue into feats of badass in later episodes.
Hideyuki Makimura, Ryo's partner in the first four manga stories (and first five episodes of the anime) had been created specifically to die, so his death would provide a reason for Ryo and Kaori's partnership. The author was quite surprised discovering how popular he was right after killing him off, and brought him back in flashbacks and implied he was the man Saeko loved, choosing him over Ryo. He even proved popular enough to receive an episode centered around how he and Ryo first met in the anime's fourth season in 1991.
Hayato Ijuin (otherwise known as Falcon or Umibozu) is this in spades, particularly after the second half of the first season began to develop his character significantly (in the first half, he was a minor character who appeared only in two episodes as simply a stoic hitman). Eventually, it reached the point where entire episodes were devoted to his antics and his appearances as a major cast member outnumbered those of other recurring characters such as Saeko Nogami (originally the most prominent recurring cast member during the first season).
Estrogen Brigade: Despite - or maybe due to - featuring a Handsome Lech protagonist who is all over any attractive woman he sees, the show owns a noticeable female fanbase.
Genius Bonus: If you know firearms you can understand many particulars before they're explained. For example, Silver Fox's return may be guessed before his identity is revealed if you recognize the Remington Model 700 used by the mysterious villain to shoot Kaori's shoe and remember that he used a rifle chambered for the .308 Winchester round in his debut (the Remington Model 700 may use various rounds, but the .308 Winchester and his military variant 7.62x51mm NATO are the most famous chamberings), and serious opponents can be recognized by their pistols and revolvers (if they use anything bigger than the .357 Magnum round and are not Umibozu or fighting him, they're idiots) and how they use them (if they don't follow safety rules, they're idiots).
Germans Love David Hasselhoff: City Hunter was very popular in Europe (particularly France, where it enjoyed a prevalent run on TV in the Club Dorothée show with the title Nicky Larson and a Narm Charm / So Bad, It's Good dub, it even spawned an original live action movie in 2019, City Hunter: The Cupid's Perfume), Hong Kong and especially Taiwan, but was only a mild hit in Japan. In the US, its fame remain limited as well, mostly due to being an older series whose anime adaptation wasn't dubbed until recently.
During a story Ryo gets a truly idiotic and half-asleep face, and, according to an old friend of him, it meant he was practically undefeatable, and the last time Ryo had that look he wiped out an enemy platoon in half an hour alone. It became really funny when Ryo's Roaring Rampage of Revenge for the villains having indirectly made him impotent for a while devastates their HQ, but becomes much harsher what had happened the previous time he had that face: he had been drugged with Angel Dust, leading to Ryo massacring an enemy platoon in horrible ways.
Ryo's fear of flying on airplanes, and even of airplanes in general, caused quite a few laughs at Ryo's expenses, even having Umibozu scaring Ryo with a toy airplane. Then Kaori remembered that Ryo is the only survivor of a plane crash...
Ho Yay: One manga story (later adapted as a two-part episode during the second season of the anime) involved Ryo's client being a female actor disguised as a man to disguise her scent from a group of criminals stalking her, although Kaori is unaware of this and falls for her male disguise. When Ryo finds out however, his perverted side takes over. Kaori later notices Ryo's eagerness to accompany his client to bed and Hilarity Ensues.
Les Yay: This occasionally occurs such as when Saeko once hit on Kaori, but keep in mind that Saeko didn't know that Kaori was a woman at the time. She admitted later that she was just screwing with her.
.357 Magnum: Colonel Johann Friedrich von Helze, "The Red Grim Reaper", is Nina Shutenberg's long-lost father, and a clever, soulful assassin working for the East Galliera Intelligence Agency. Once in love with pianist Sofia Shutenberg, Helze used his relationship to secretly carry out his hits, only to be driven away from his future family by Sofia's father Klaus. Tasked by Ambassador Bondal to acquire documents that could expose his shady plans, Helze kills Mr. Kilhiman to prevent a fake assassination attempt as he easily steals the case containing the documents. Hired to kill Nina to acquire the rest of the evidence, Helze does what he can to prevent those from killing her, even getting Ryo and City Hunter to save her from a kidnapping. Freeing a captured Klaus and Kaori from Bondal's clutches, Helze later makes a deal with Ryo to fake his death during a duel, just so he can remain by Nina’s side and make up for the last twenty years he's been away from her.
Goodbye My Sweetheart: "The Professor", Emi's nameless brother, is a terrorist who waged war against the entire world after being left to die in the Gulf War. Killing his commanding officer afterwards, the Professor heads for Shinjuku with intent to hold the entire district hostage for 10 billion yen. Breaking the convicts Satoru and Tatsuoka out and recruiting them by proving his strength, the Professor has them craft bombs to be placed over Shinjuku, making the district’s new train system act as the trigger to activate the explosives. Using the yen as a distraction by calling out its location and having the cops trampled by a mob of civilians, the Professor kills Satoru just as he's about to disarm the train bomb. Shot by Ryo in a duel, the Professor uses his final breath to request Emi to smile, requesting his sister's happiness to be the final thing he sees before he dies.
The manga and anime can be viewed as if it were written by Shane Black in vein of Lethal Weapon (which was released the same year the anime came out - 1987).
To Lupin III. Think of Ryo as a mix of of Jigen and Lupin (a sharpshooter with an eye for women) and Saeoko as a mix of Zenigata and Fujiko (a manipulative female in the police force).
Woolseyism: Ryo's catchphrase, "mokkori," is the Japanese word for boner. When ADV Films dubbed the series, they made the decision to translate it by using the word nookie (Sometimes spelled as nooky), which is another sexual term, but considered not as explicit as boner. Thankfully, fans didn't seem to take issue with it, finding it just as funny and memetic as mokkori. When the Shinjuku Private Eyes movie got dubbed, Sound Cadence Studios, who was tasked with dubbing the movie, preserved a lot of the original dub's writing and original quirks, nookie included.
[ Ai Yo Kienaide]], the anime's first opening theme, definitely qualifies. It's well sung with a catchy tune that also captures the sweeping feel of Tokyo's vista and Ryo and Kaori's reliance on one another, all while encapsulating The '80s perfectly.