In the opening cutscene of Mission 1, there are times when Nero's bullets seem unusually slow when they approach Dante. The best example happens when Nero shoots at him after saying "I won't hold my breath" — The Bullet Time visual effect is actually present, but because it happens in a split-second, it creates an illusion where the bullet is suddenly set in slow-motion while Dante moves at regular speeds. Obviously, this sequence demonstrates Dante's superhuman reaction time, but it can also justify what happens immediately after. Nero somehow shoots low at the spot where Dante's feet were standing on, but if you replay that part in slow motion, Dante crouched low enough at that same spot before jumping. This means Nero is correctly predicting Dante's movements and trying to react fast enough to them, but the guy is still faster than him.
Devil Arms are typically powerful weapons created from demons, usually seen as melee weapons (with some exceptions like Pandora, Geryon, and the Doppleganger). Unlike Dante, Nero never uses any Devil Arms, but it isn't necessary because he literally has a devil arm.
In-universe, Nero is named after the black blanket that he was wrapped with when he was found outside of an orphanage, as the word "nero" means "black" in Italian. However, there are other things that imply Nero being named after the Roman emperor:
The historic Nero was a poet, and so was the author of The Divine Comedy, Dante. This makes his name another case of Theme Naming.
Credo, Agnus, Sanctus, Kyrie, and Gloria are all named after the different parts of the Roman Catholic "Ordinary of the Mass". Their naming actually makes a bit of sense. Nero was a Roman Emperor well known for persecution of Christians, and the Order, with whom he is in conflict with, are all named after elements of the church. In DMC4, Nero is the "rebellious" member of the Order of the Sword; he doesn't actually adhere to what they're worshipping, he's just there for Credo and Kyrie.
Emperor Nero was widely believed to have started the Great Fire of Rome. DMC Nero's signature weapon, Red Queen, has an Exceed system that ignites the sword with flames.
Also, all of the aforementioned Order of the Sword characters (Credo, Agnus, Sanctus, Gloria) who use demonic power have names that are Latin words, as opposed to the only pure human, Kyrie, whose name is a Greek word.
Another (funny, but probably inadvertent) bit of Bilingual Bonus theme naming: "Kyrie" comes from the Greek phrase "Kyrie eleison", "Lord have mercy". Except in this game it's the name of a woman. "Trish" comes from the name "Patricia", which in turn comes from the Latin "patrician", the original group of aristotic families of ancient Rome. There are three named female characters in this game, and if you know enough classical languages, all three of them are named "Lady".
Nero fights and defeats the toad demon Bael, and they happen to share the same color theme (Nero's clothes are primarily blue while Bael has blue Rusalka feelers). The similarity also happens in the match-up between Dante and Dagon (Dante wears a signature red coat while Dagon has red Rusalka feelers).
Bael is a toad-like demon who can lure victims using female humanoid baits (called Rusalka), and hide in a thick fog, seemingly turning invisible. In demonological grimoires like The Lesser Key of Solomon, Bael is a demon depicted as a man, cat, and toad hybrid, and has the power of invisibility.
Although the protagonists easily figured out that the Rusalka feelers are demons, Nero's completely unfazed reaction to their seductive moves can also be attributed to him having romantic affections only for Kyrie.
Nero has several moves named after gambling terms (Double Down, Maximum Bet, Roulette Spin, High Roller). And then you realize in the main campaign that he's the only one who has to play that damn Dice Game, driving any "gambling" reference to another level.
Echidna the She-Viper is perhaps loosely based on the serpent women from Classical Mythology. She appears as an attractive humanoid woman protruding from the venus flytrap-shaped mouth of a huge flying demonic serpent thing. Echidna can birth other demons and control plants, which is probably inspired by the fact that serpents are seen as symbols of fertility in certain cultures. While it could be a coincidence, Dante acquires a cool weapon called Gilgamesh after defeating her, which is a reference to the serpent sent by Ishtar which stole the divine immortality herb.
The legends of Sparda state that he fought against legions of demons by himself. A difficulty mode in this game actually allows you to fight of legions of demons by yourself. The name of said mode? Legendary Dark Knight (Bonus points if Dante is using the Sparda costume).
Nero effortlessly blocks Dante's Rebellion with his Devil Bringer arm... twice, including Dante's Signature Move; Stinger. Later on, Sanctus easily stabs said arm with the Yamato. These scenes create the implication that Yamato is sharper than Rebellion, which seems contradictory considering the several times Dante and Vergil's swords clashed in 3, and on equal footing. However, it could also be justified because the Yamato's Flavor Text in DMC3 states it can cut through anything.
Nero could (theoretically) use his Devil Bringer to save Kyrie on at least two occasions, especially by snatching her from the captors. However, you only use the Devil Bringer in-game as a grappling hook against non-corporeal targets, or to lay the smackdown on the bad guys, neither of which requires a delicate touch. Perhaps the Devil Bringer is incapable of being used in a gentle manner? He might've intentionally avoided using it, fearing that he might accidentally harm her.
Also, rewatch the cutscene in which Kyrie first sees the Devil Bringer. Nero tries to hide it behind his back, which would be hilarious if it weren't so tragic. He doesn't even want her looking at the mark of his curse (as he sees it), let alone coming into contact with it. It was no accident that the final cutscene of the game had Kyrie interlacing her fingers with those of the Devil Bringer — it was the ultimate sign that she had accepted Nero for who he was.
Nero's Buster (especially its stronger variant, Devil Buster) deals more damage if the player mashes the grab button. Button-mashing encourages an aggressive reaction from the player, and implementing that mechanic to Nero fits so well because he has the most aggressive personality among the five playable characters.
In the second Nero vs. Dante battle, Nero's final attack is identical to the one Vergil used in 3 to defeat Dante. However, Dante dodges it and stops Nero. This shows Dante became more skilled and has learned from his fight with Vergil, thus he won't fall for the same trick twice. Although it's also ridiculous that Nero would know Vergil's attacks, it could have been made to hint that he really is Vergil's son.
The fact that Nero fights Dante in this game multiple times is, in and of itself, a hilarious case of Foreshadowing mixed with a Mythology Gag to both the first game and 3. Who else but Vergil's own son would have some sort of hyper aggressive beef and repeatedly pick fights over the course of a game with Dante?
One peculiar trait of Nero is that he swings Red Queen around with just his left hand for a majority of his attacks. It seems like a pretty odd way to make him distinct from Dante. However, it may have served as a subtle connection to another character. Earlier in 3, Vergil is shown wielding another BFS of the series, Force Edge, with one hand. Considering that Nero seems very similar to Vergil, perhaps this was done to further establish some relationship between them.
There's also the fact that his right hand started in a sling and ended up a demonic claw, he might just be using his left hand to swing Red Queen and fire Blue Rose since it's still human and easier to use them.
It gets even better on the few occasions Nero wields both Red Queen and Yamato at the same time. What other character in the franchise has been shown to use a similar combat style?
Lucifer having a rose to detonate its red blades can be symbolic in a way. Lucifer's blades look like darts in-game, but without the visual effects, they look like thorns or spikes. The stem of a rose is covered with sharp thorns, and there's even a trope for roses representing beauty and tragedy. The Devil Arm and its blades being primarily colored red is also visually thematic for the red petals of its own rose.
Dante letting Nero keep Yamato; by most laws of inheritance, a deceased person's possessions go to any offspring before siblings. So as Vergil's son, Yamato rightfully belongs to Nero, not his brother Dante. Dante knows this and is just using It Was a Gift as a convenient excuse to give it to him; Nero's not quite ready to learn who his dad was and it avoids the subject for a while.
It's kind of symbolic how the three boss fights from the Order each have different demonic post-Ascension Ceremony forms based on their interpretation of Sparda. Credo and Agnus both see him as a holy savior, so their forms have dominant light colors. While Credo has a purely angelic form because he sees Sparda as an Ascended Demon, Agnus has an insectoid form similar to how Sparda's wings actually looked, because Agnus is more interested in the demonic side of things. Compare and contrast Sanctus, who fully acknowledges that Sparda is a demon, and as a result, has a darker color theme and grows horns for his "Diabolica" form in the Final Boss fight.
In the case of a song having a meaningful name upon analysis, the track that plays over the ending, "La Vita Nuova", takes its name from the collection of Courtly Love poetry written by the historical Dante. This works on a number of levels; first, the song plays over the start of Nero and Kyrie's new life together; second, Kyrie's acceptance of Nero as he is marks the signing and sealing of their love in a way that the Dante of the poems could not attain; third, as was common in Courtly Love poetry, the love being celebrated brings the protagonist closer to the divine.
Sparda is still Shrouded in Myth even if the Order of the Sword views him as their god, so much so that his son Dante mentions "there's a lot of confusion surrounding him". A line from Nero in the final mission also reveals that Sanctus doesn't know what made Sparda powerful. Even if the Order got some facts wrong, their own version of Sparda still worked to their advantage of attracting the masses. After all, if the ordinary citizens don't know much about Sparda to begin with, they have little to zero chance of going against the Order's teachings. It makes Nero's speech even more meaningful in retrospect; as someone who shares the bloodline of Sparda, it makes sense for him to go against the Order because he has a better understanding of Sparda's past than Sanctus.
is a demon depicted as a man, cat, and toad hybrid, and has the power of invisibility.