$12,659 per year on groceries works out to roughly $240 per week. While it is possible to reach that (e.g. by shopping exclusively at high-end specialty grocers and avoiding coupons), most families would pay far less. A family with access to a supermarket would probably spend around $80-$120 per week on groceries, or $4200-$6300 per year.
The car expenses assume a very large fuel-hungry vehicle, and appear to assume the vehicle will be purchased on a high-interest loan. A five-seat sedan would work just as well, and would result in expenses of about $3000 per year ($10k amortized over a ten-year operating lifetime, plus $2k per year in fuel).
Similar issues exist with the other large expenses. For example, the author's chosen goal for college savings is higher than the cost of a four-year degree at Stanford (according to the stanford.edu Net Price Calculator) and is far more than tuition costs at a normal school.