Yes, but a miniscule amount. Less I think than the difference in gravity at the equator than the poles from the earth being a slightly flattened sphere.

I have nothing off hand to back this up, but from what I remember of physics, gravity is slightly greater at the poles, but not (directly) because of rotation. One of the variables used to determine the acceleration of gravity is the distance from the center of the earth. Since the earth isn’t a perfect sphere, the poles are closer to the center than the equator. So there’s a bit more gravity. But not enough to notice.

The same, of course, is true with varying altitudes.

I have worked at a scale shop on and off for a few years (on at the moment). We often deal with very high end balances and the differing gravitational constants occasionally come up. More often, however, it’s the difference in air boyancy from place to place that causes signifcant weighing errors.

Centripetal acceleration is w[sup]2[/sup]r, where w is the angular velocity and r is the radius of the circle. The Earth’s radius is about 6,378 km, and its angular velocity is 2 pi radians / day, or about 0.0000727 radians / second. Squaring that and multiplying by the Earth’s radius in meters gives us a centripetal acceleration of approximately 0.0337 meters per second squared; about 0.3% of the force of gravity.

Off the top of my head, I seem to remember that gravity is strongest in Northern Norway and weakest in East Africa.
People have mentioned that the oblateness of the Earth and its rotation account for the variations in gravity. There is a third factor - the density variations of the Earth at differing locations. Granted, this produces slight but significant differences.

As far as scales showing different weights on different locations on the Earth, wouldn’t balances be a more accurate determinant of mass?