Silver doesn't do anything to vampires. Silver bullets are (per Universal Studios) the only way to kill werewolves (wolfsbane will ward them off, but won't kill them).
According to legend, vampires cannot cross running water. Not sure what the rationale is there, but that never seemed to stop any literary or cinematic vampires. Holy water will cause first- or second-degree burns on a vampire, but probably won't do one in.
But the perfect execution of a vampire is, "Stake through the heart, Garlic in the mouth, cut off the head, and burn it."
You forgot "and bury the corpse at a crossroads." Indeed, you forgot "crosses" from your list entirely. Crosses don't necessarily kill vampires (although a cross driven through the heart is a good substitute for a stake), but they are pretty good at keeping them at bay. Mirrors don't affect vampires, they just give them the creeps because they don't show a vampire's reflection.
I've never heard anything about salt or fire being particularly efficacious against vampires. Fire is used to kill (or at least freak out) Frankenstein monsters. Salt is used to kill garden slugs.