John you need a good beating after that one.
A few problems. First with the original answer. Heres a properly linked url http://www.straightdope.com/mailbag/mdownup.html The content was fine, but I am curious why the most obvious answer was neglected. Now a couple of definitions you use are reasonable, normal=down, and direction of gravitaional force=down, but the definition that is most practical in scientific use is that down and up are simply arbitrary vectors. These vectors of +z & -z can be set at any direction that make logical sense (or not for that matter). On Earth the most common answer is relative to the force of gravitaion, unless you digging a hole “down” then down is perpendicular to the level of the soil at that point, or climbing a mountain then “down” is the direction parallel to the slope of the incline. Granted these last two definitions are imprecise and subjective, they still are as applicable as the plum bob explanation. So I submit that the most correct answer to this question is the arbitrary z axis. One arguement to why I say this is so is that if two astronauts are cunducting an experiment in space I suspect that they would use the term down to describe the direction towards the floor of the module, or possibly towards their feet if they are floating.
Pleonast, its the lack of centripetal (not centrifugal) force, centrifugal force doesn’t exist, its merely apparent. And acceleration due to gravity isn’t important here, the direction of it is. g is a scalar constant. The plum bob measures the direction of this force, and the bob will be slightly affected by the lack of centripetal force (angular acceleration) in a direction parallel to the plane of the equator, but on the equator the effect is non-existant. At the equator this force acts in a direction opposite the acceleration due to gravity, and reduces the apparent gravitational force, and depending on what lataitude the measurement is taken at it alters the dirction of the gravitational force by vector addition, but it has no change on the acceleration due to gravity, just its apparent results.
Finally this result is not measured as simply as you imply. You overlook the fact that the rotation of the Earth is about its center of mass, one of the operative definitions centers around the center of the geometrical shape of the Earth. These points are not concurrent. Also since the radius of rotation will decrease as you move away from the equator the effects of the angular acceleration get increasingly low. The flattening of the poles magnifies this reduction effect as well.
Auraseer is correct that the plumb bob acts in the same direction as down by the most practical definition on Earth, and that he angular acceleration is already included in the plumb bobs direction.