Mouths: Although folklore has it that the vampire sucks blood through the fangs like a straw, it really doesn't work that way. The teeth are just can-openers, and the rest is all hickey-action. Due to the reinforced pattern of the fangs, as long as they are kept in the victim, the blood won't begin to clot. The feeding process is a matter of poking two holes in the person, then wiggling the fangs about while sucking the free-flowing blood. Generally, a vampire releases a thin solution of vitae that cuts down on most of the damage that normal gnawing would do and also produces the 'Ecstasy Effect'. Once the fangs are taken out of the victim, a vampire can increase the concentration of the Vitae-solution slightly so as to have the surface skin heal over (although there still are internal injuries and hemorrhaging underneath). Applying this solution to a non-fang injury can produce the 'Ecstasy Effect', but can't actually heal any non-fang damage (since the fang-damage was done with this solution already applied during the entire process) unless one has Obeah:1.
Sweetmeats: For the most part, the internal organs of a vampire desiccate, atrophy, and wither as time passes after they were Embraced. Pretty much all that remain are the brain, heart, lungs, stomach, and circulatory system.
The brain still keeps the same functions as it did before, although without electromagnetic impulses (A psychic can still read a vampire's mind although it's a little weird, Mage Mind Effects still work on them, but a CAT scan or an EEG will turn up no activity). Should the brain be removed from the rest of the body, it only survives as long as Vitae remains in it (it tends to pour out of the neck, there's nothing to process blood-to-Vitae, and the Blood Pool is severely lowered). Without a connection to the heart, there's no way for the vampire to get extra Vitae to it to perform 'special effects'. Destruction of the brain results in final death and a headless corpse full of Vitae. Although the heart doesn't beat any more, it is still the means for the Vitae to get around by means of a slow undulating (not unlike a crawling slug or snail), and damage to the heart can complicate any 'special effects'. Destruction or removal (except with Serpentis:5 or suchlike loopholes) of the heart results in Final Death. When a vampire uses Vitae more than just to stay active, the physical activity of the heart increases (although like the brain, there's no electromagnetic activity).
The lungs still retain the same job as before, save for oxygen-supply. With no need for breathing, they're merely a way to get air across the vocal cords or to make suction for blood-sucking. Blood and water that enters the stomach is drawn into the vampire's tissues, mixing with the Vitae that is slowly oozing through the veins and arteries, although non-blood is left behind to sit and rot unless expelled back up.
To properly stake a vampire requires wood (a magical footnote in the vampire contract), and results in a vampire unable to move or pump blood. To improperly stake a vampire with non-wood only results in a damaged vampire that has a hard time pumping blood and is extremely ticked off.
Nervous System: With the lack of electromagnetic activity in the brain, one might wonder just how the vampire is able to get both signals to the limbs from the brain in order to move around, and from the limbs to the brain to feel around; The brain is normally a processing center for the electrical impulses sent up the nerves and back down again. With the state of 'unlife', this system is changed such that the impulses are sent up and down the vascular system, along the continuous vitae within. Much like how if a nerve is severed (or traumatized) in a living person, if the flow of vitae is cut off from a limb in a vampire, that limb becomes both numb and paralyzed (mind, it'd take a -LOT- of cutting off. A tourniquet would have to be frightfully tight to do the trick). It is in this manner that a damaged vampire's actions can suffer from 'Wound Penalties', and yet a vampire cannot really be stunned due to massive trauma (unless it is so massive as to disrupt the flow of vitae from the brain and heart to the rest of the body).
Although this normally requires a continuous vitae connection, a few Disciplines and other 'Vampiric Special Effects' are able to find loopholes in the system (RE: Blood Bonding, Quietus:3, Serpentis:5, Thaumaturgical 'Path of Blood':5, Thaumaturical Ritual 'Communicate with Kindred Sire', most all levels of Sanguinus, et cetera), leapfrogging thoughts or powers across remote distances by means of sympathetic magic that connects two amounts Vitae from the same being, or from the same Clan (which may explain why Clans tend to 'inherit' aptitude for particular Disciplines), or merely from the connections that bind all Vitae.
What I'm not sure about is if any of these above notions would allow folks to get away with things they ought not to.
On another note, if there were a painting 'Portait of Freud as a Young Lady'.. should Freud be holding a dachshund in his lap, eating a hot-dog, sitting in a train, some combination of those, or 'other'?