<pendantry>
There is no Planck second. There's a
Planck time, however, and I presume this is what you meant.
But even that cannot be correct. It presumes that the sun illuminates exactly half the moon, and that the viewer must be at a specific point (or line) in order to see this half and nothing else.
But this fails for multiple reasons. First, the sun will illuminate slightly more than half the moon, because the sun is not a point source. Second, we can see slightly
less than half the moon. Third, the variation in angle of our line-of-sight cannot allow for a full moon at only the point where we view the illumination of the moon symmetrically, because that would require that the line of sight and the sun-moon line to be parallel and overlapping. But that can only happen during a lunar eclipse. Every other time there is a "full moon", there is always a measurably nonzero angle between our line of sight and the line between the center of the sun and moon, because the moon is out of the plane of orbit of the earth around the sun.
Our definition for what counts as a full moon must therefore include a nonzero angular tolerance to at least account for each of the factors I listed above. I haven't crunched the numbers so I don't know if that would extend the relevant period to second, minutes, or hours, but it's definitely going to extend it past a Planck time.
