Infinitely high wall

Someone in /b/ posted the usual "infinitely high impenetrable wall separates you from sex/money/delicious cake" thread, and it got me thinking. Would an infinitely extending plane of uniform density have infinite gravitational pull at it's center of mass, or is it asymptotic depending on thickness? At first I thought I could consider it as a single point at the center of gravity of infinite mass... but then if it extends infinitely, IS there such a thing as a center of mass? can we declare an arbitrary center of mass, e.g. under the feet of an observer? I would think that as any portion of the plane exerts a force at the inverse square of the distance, we could assume that past a certain distance the force is negligibly small, but then again the number of points at that particular distance increases at the square of that distance. I think its safe to assume that all vector components parallel to the plane would cancel each other out, and that the perpendicular component (into the plane) decreases with distance as the angle gets smaller, but assuming a wall of none-zero depth, that angle never becomes zero.

Furthermore, what sort of tidal gradient could be expected? And how would this scenario change given an open or closed universe? I think in a closed universe, you could treat it as just being inside and infinitely large sphere, in which case everything cancels out (think "Hollow Earth") and there should be NO net gravitational force... but then again how could one differentiate the "inside" and "outside" of such a sphere?

is this applicable?
http://en.wikipedia.org/wiki/Gauss%27s_law_for_gravity#Bouguer_plate