Nope, this isn’t a need answer fast question. 
Apparently, temperature and chemicals are the two factors in embalming. Already we’ve seen some bodies in the Arctic or Himalayas pretty well preserved. What if a body were to be kept in absolute-zero temperatures, after first being thoroughly soaked in preservative chemicals? Might it still be near-perfectly preserved a thousand years later?
Plastination seems to result in a fairly durable and high-quality end result.
ETA: I’m not sure that ‘absolute zero’ means what you think it means.
Mao, Lenin, and Glorious Leader Kim Il Sung IIRC were all embalmed and put on display for decades. Mao looks pretty good. I read somewhere once that one of the three (Kim?) the job was not done well and at one point an ear fell off. Apparently wax is useful to cover up issues.
The problem with freezing is this - water expands and crystalizes. This wrecks the cells as the ice crystals destroy the structure; fortunately being solid helps keep it all together. Once you get significantly below freezing, temperature is not important. There’s really no point in cooling so low that even the air the body sits in is liquid (or solid). I would hazard a guess the ideal low-temperature treatment would be to replace as much water as possible with something that does not cause crystallization damage. Probably better off embalming with bacteria-killing fluids and using a cool but not freezing temperature if looks are important.
If a body was kept at absolute zero, you wouldn’t need any chemicals to preserve it forever.
Pope John XXIII was looking pretty fresh 50 years after his death when we visited St. Peter’s a few years back (apparently the Swiss Guards’ atheist-sniffing dogs were off duty that day). The other pontiffs-under-glass not so much (one was pretty freaking grisly looking).
I suspect that’s not true (that a body kept at absolute zero will be preserved indefinitely). Flesh and bone, even of a corpse, are not meant to get that cold, and I would expect damage to occur well before you got that low of a temperature.
What kind of damage are you talking about?
The biggest threat to displayed corpses is decay. I can guarantee that there won’t be any microbial action at Absolute Zero.
Also, the corpse will be almost rock-hard due to the frozen water, so it should be pretty sturdy.
If you left the water in the body then you’re going to have crystalline damage, as md2000 notes above.
So?
On a molecular level, what do you think causes more damage? Ice crystals or embalming fluid?
I’m not quite sure what the actual question is, and what “ultimate” condition means. Embalming is a form of preservation with specific goals; there are different types of embalming and body preservation.
I believe the most common type is for run of the mill regular people who will be put on display in a casket for a funeral service, and the goal is to keep them looking normal for a few weeks max; and generally even then just their face/head/hands. You can touch them up with make up to get them picture perfect, and then you drop the project into the ground and forget about it.
Then you have the super-prominent figures meant to be put on display for decades or longer; also meant to look natural. I think the physical/chemical treatment as well as maintenance routine is significantly more involved and expensive for that. You don’t want to be opening up their containers every week for touch-ups, so the treatments are quite a bit different.
Contrast that to ancient embalming and/or mummification, where the goal is to keep the body from decomposing, but it’s actual appearance isn’t important. These bodies get dehydrated, painted over with resins, and wrapped up. They can last for thousands of years but sacrifice the natural look.
So it depends what your goals are; do you want the body to appear “fresh” and almost-living? Probably best to do a chemical treatment and avoid freezing & cell damage, and limit things like UV exposure. If you want to preserve some portion of the biological tissues without altering their chemical make-up for later use but don’t care what it looks like when you thaw it out, freezing might work better. Freeze-drying has it’s advantages as well, but the bodies in the Himalayas eventually dry our from exposure to air, and bleach out from the sun. Many methods of tissue preservation are not compatible with each other however, so you need to know what your goals are.
Well, as far as freezing goes, Otzi probably holds the record.
According to Wiki-5300 years. For a fellow that old he looks pretty good.
Wiki says he’s “Europe’s oldest,” which begs a questions. Be that as it may, he may be older than the Tollund Man, but nobody in that crowd looks at you like he does: Tollund Man - Wikipedia
What I mean by “ultimate” is that the preserved body looks as much intact and recognizable as the live body as possible.
Sure, but to what extent does the end product need to contain the ‘original’ materials of the corpse?
For room-temperature display, it is generally the case that: the more you replace, the better the preservation.
If you replace the water and fats in the corpse with resins (plastination), you can achieve a remarkably good-looking end result, but is that ‘preservation’? (in replacing maybe 80% of the corpse by weight - is it still the same thing?)
If you replace 100% of the corpse (e.g. a statue or waxwork), then the end result can be incredibly lifelike.
I recognize this philosophical question: Theseus’ corpse. How much of a corpse can you replace before it’s not that corpse any more?
Good point - let’s say the body has to be chemically soaked and frozen as is, no removal of tissue/organs.
Does cryonics count as what you mean by “preservation?” Theoretically, the preservation is good enough for future revival (through some yet-hypothetical technology). It’s not a no-maintenance process, though - ya gotta keep changing the nitrogen!
And from reading the Wiki article, it sounds like the internal state of these … patients is largely unknown (presumably because messing around with them kind of defeats the purpose):
Freeze a tomato then thaw it out and get back to us. Ice crystals will do massive damage to the tissues of a water filled object.
Eat the embalmed one, and get back to us.