ASOIAF: Why is there so much emphasis on the stench of Tywin's corpse in A Feast For Crows?

It works on several different levels.

But it should be clear: it is a mystery. Pycelle claims to have removed many of Tywin’s organs, to stave off the rot, and I believe him. But it’s not only the smell…it is the fact that he is literally decomposing at a faster than normal rate…his mouth twisted into a hysterical grin, his skin splitting and oozing fluid….

I mean, the metaphor is clear. Tywin Lannister stinks. Tywin Lannister was rotten.

And I actually think that is the main thing.

GRRM is showing his personal contempt for a character who forced his own son to participate in the gang rape of his own wife.

It’s not that subtle, either: just as Arya Stark is constantly associated with water and baptismal imagery, Tywin Lannister is consistently associated with shit in the books.

1. First of all, there is the infamous “Tywin Lannister shits gold” meme, that Tyrion reflects upon in Game of Thrones and comes up here and there throughout the series. And ends up being an elaborately set up punchline to his death.
2. When Arya first approaches Harrenhal ,she is assaulted by the smell:
   
   'The stink of the Lannister host reached Arya well before she could make out the devices on the banners that sprouted along the lakeshore, atop the pavilions of the westermen. From the smell, Arya could tell that Lord Tywin had been here some time. The latrines that ringed the encampment were overflowing and swarming with flies, and she saw faint greenish fuzz on many of the sharpened stakes that protected the perimeters."
   —A Clash of Kings
3. After the Battle of the Blackwater, Tywin’s ceremonious display of majestically entering in full panoply and honour as the “saviour of King’s Landing” is marred by the horse he rode in on shitting on the floor. (Fuck them both, by the way.)
4. And, of course, most obviously, there is the fact that he is killed on the crapper in the midst of a leisurely shit by his son —fitting, since he had shat on Tyrion all his life; and seeing as how he had made Tyrion clean out and unclog the plumbing system at Casterly Rock, I am probably talking literally.

(There may be more: I remember reading a list once compiling the associations.)

Beyond that, if you’re looking for a non-meta-explanation, there is the theory that Oberyn Martell may have poisoned him at the dinner he had with him, using the poison that basically constipates a man, until he dies from a build up of…foul substances. It is a plausible theory that MIGHT explain the smell: I am not a medical doctor so I can’t be sure if this is how it works, but, you know, maybe the built-up shit permeated him on a molecular level or something.

It’s one of the best minor theories and is well-liked by many fans, even it it’s ultimately unnecessary for the story.

Or perhaps the gods are subtly making their opinion of the Lion of Casterly Rock known.

Tywin’s spirit ought to be grateful for his rot. Weird things happen when Lannisters lie dead in state: at least the stench kept Jaime and Cersei from getting blood all over the coffin.