All this is from memory, having seen an opened up Model S pack and BMS, and having designed commercial lithium management systems.
I didn't see anything to allow them to disconnect individual dead cells, I suspect they just let them ride along with the good ones. They're in large parallel groups, so a single bad cell wouldn't have a huge effect on the rest. Each cell has a mechanical fuse for over-current protection, which is basically just a wire welded between the cell tab and parallel connection bar.
Regarding balancing, they use TI BQ76PL536A-Q1 ICs (one for every 6S cell block), and approximately 40ohm of shunt resistors per parallel block. There are a couple of things that let them get away with such a small resistance for balancing. First, they use high quality cells, which are probably very closely matched to begin with. Second, they connect 70 or 80 of these in parallel (I forget the exact number). Assuming that the cells are well matched to begin with, the more parallel cells you have the closer to the population average you'll get. The end result is a large "cell" that, thanks to statistics, is a very close capacity match to it's companions. If you had 100% identical cells in identical conditions (obviously not realistic) you'd need no balancing after the initial one. The Tesla cells obviously aren't perfect, but are going to be closer than the consumer grade stuff most people are used to.
It's not just about the BMS. Cells, temperature management, load management, etc also play a role in overall pack reliability. Having worked with the same parts Tesla is using, I can say that we all could have a similar battery system to Tesla's, but few would want to pay for it.