I'm not an accountant, but if I'm reading this correctly, Zuckerberg received 120 million shares at 6 cents each in 2005. A section 83(b) election requires him to purchase those shares first, which would have cost ~$7 million. Additionally, if the options' market value was higher than purchase price, he'd have to pay taxes on the difference.
In order to apply to options, 83(b) requires (among other things) that the options be readily valuable at the time they are issued. In FB's case, it is likely that the stock options could not be valued (i.e,. because they were not publicly traded and there was not a recent valuation study).
See the Regulations to 83(b), which provide a lot more detail about the applicability of 83(b) than the statute itself, especially Treas. Reg. 1.83-7 (regarding stock options).
