Alfred and Alexia from childhood have had an obsession with ants and dragonflies. Claire sees a movie early on, where the twins as children pluck off a dragonfly's wings and drop it into an ant farm to be slowly devoured. The motif repeats itself a couple of times in a couple of ways throughout the game, ending in a final battle that's pretty much a replay of the home movie.
Alexia's ultimate death is an almost perfect mirror of the home movie Claire and Steve discovered in the "Rockfort Mansion" and plays nicely into her deluded obsession with ants, making it full of symbolism and maybe even something of a Karmic Death.
Alfred's being a terrible shot despite having a laser-pointer-equipped sniper rifle is an almost Genius Bonus level Shout-Out: the exact same model of sniper rifle appeared in George A. Romero's Dawn of the Dead film, where Peter notes that "The only person who could miss with this gun is the sucker with the bread to buy it.". True enough, Alfred is rich enough to buy such an expensive gun, and he is completely incompetent at using it.
It isn't an immediately familiar concept to Western players, but Claire's alternate outfit in the Battle Game is that of a "race queen," a promotional model used in Japanese racing and auto shows. It comes complete with the Umbrella logo down the hip of her shorts.
Code: Veronica made the knife a viable offensive weapon for the first time. The first game's knife was a dinky little pocketknife, this one's a step down from a machete!
The Ashford twins are the foil to the Redfield siblings. Claire and Chris are fairly stoic, dark haired, good, firearm proficient and fighting monsters frequently while the Ashfords are bizarrely emotional, blonde, evil, either crap with guns or reliant on mutant powers to fight and either creating monsters or becoming them.
Of course the Ashfords would have a base in the Antarctic, because the abbreviation makes it an Ant. Base.