Pizza is an ongoing gag in the Devil May Cry series since DMC3. Staff reported ordering mostly pizza for food during the game's development.
Many of Nero's moves are named after casino and gambling lingo such as, "High Roller, Maximum Bet, Roulette Spin, Double Down, Hold, Split" etc. It is also interesting to note that a roulette wheel's numbers 1-36, when added into one another, add up to 666 which is relevant to the game's theme and also to Dante's weapon, Pandora's Box which can transform into 666 different forms.
The names of the characters who are part of the Order of the Sword (other than Nero) are all movements of the Ordinary Mass in Catholic worship: Kyrie, Gloria, Credo, Sanctus, Agnus (Dei).
When Nero fights Bael (the giant frog) it has blue bait, mirroring the colour of his coat. Likewise, the bait changes to red when fighting Dante who has a red coat.
Nero's Devil trigger ghost looks similar to Vergil's devil trigger in Devil May Cry 3. It can be seen performing Vergil's katana strikes with Yamato.