Right now the car is still evolving--both design and manufacturing is changing (literally) daily. It doesn't make sense to use robots yet.
Source: I toured the factory last week.
I'm not sure though.
Generally people don't start building/buying robots to do this stuff until the economics forces it. That probably doesn't happen until they sell a million or more cars per year.
EDIT: This is factually incorrect as Tesla does employ a lot of automation. But there are still plenty of people in the loop as well.
My dad did design work for division of Tyco that made syringes. That was fully automated. 100,000sqft of production and a single janitor automated.
Tesla? Definitely a lot of people visible. http://www.flickr.com/photos/77735091@N08/7398173016
Given those restrictions, from a mfg background and looking at the pix its basically more or less similar to other automobile plants, not particularly under or over capitalized. Their "secret sauce" is not their shop floor. Note I'm not in any way implying there is anything wrong or imperfect with their shop floor, I'm merely claiming that the production floor is not their "secret sauce".
This is probably by design. If you're going to push the boundaries in numerous areas of technology, it would be pretty dumb to push your luck and in addition to everything else, try to hyper automate a factory. If anyone would try a hyperautomated factory, I would guess it would be one of the giant incumbents, probably Ford, probably on a known and simple/cheap model. I would expect the worlds first "never touched by human hands" automobile to be something very similar to a Ford Focus rather than a Tesla.