Pros
Career advancement beyond Stanford, in my position career advancement would require graduate training (which I intend to complete following this position). Benefits, support, and training opportunities within the school are better than anywhere I know of. The access, should you have the time, to other opportunities and researchers is great. It will look great on a CV and there is certainly, at least where I work, a strong emphasis on work-life balance and health. There can be a competitive atmosphere which can be a positive or negative thing depending on your position. There is a wide array of experiences within the school, so this may not be representative of everyone's experiences.
Cons
There are very few downsides, in my experience and view, of working at Stanford. The downside, were I looking to make this a long term position or career, would be a difficulty in advancement and compensation. I passed up opportunities for higher pay for the position at here, however the trade off was for better experience and a stronger CV. Advancement seems tenuous as there is a lot of competition for most jobs, or at least it seems that way. Pay advancement (although the economic climate makes that difficult most places) and increase in position title just doesn't seem like something I would accomplish very easily.