SF Chronicle had a good overview[0] of what could be going wrong. From the article:

The tower was built using a concrete frame instead of steel. Which is much heavier - it puts about 4.75x the amount of pressure on the soil below the building (as compared to other steel framed buildings of similar size).

It appears that some of the sinking could be due to weight and changing soil composition (less moisture and nearby excavation).

[0] http://www.sfchronicle.com/bayarea/article/Sinking-Millenniu...

I'm curious: How many other buildings over 20 stories in the SOMA neighborhood use friction piles? Why would anyone use bedrock piles if they are more expensive and have no "superior" advantages? How many buildings with bedrock piles in SF have tilted this much as they have settled in?

I'd say it's less about piles going to bedrock and more about the ground itself.

Building on sand, trash, and whatever other gunk comprises San Francisco ground...

You could say whatever you like, but none of the other tall buildings in SF are sinking noticeably, which suggests your theory may itself lack a solid foundation.

IIRC, a potential confounding factor was that this building is much heavier and has a smaller footprint than standard.

Are the pilings for those other tall buildings in the bedrock?

Depends. Some are but but in recent years it's been more common to use steel structures which (being lighter) don't require that.

Noise might have something to do with too. The last building that I recall having bedrock-depth pilings involved loud shuddering bangs through the financial district for nearly a month. Like you could feel it through the ground 3 blocks away every time they dropped the hammer..

that's why you go down to the bedrock, because the earth in between is not strong/stable enough. also, while much of eastern SOMA is indeed landfill of the bay, this particular building is far enough inland and would be within the original SF coastline.