The obvious limit on the resolution of the camera is directly related to the F-number (N)

N = ƒ/d

where ƒ = focal length

d = diameter of the apperture

The limit in resolution caused by light going through the hole from two places and ending up in one pixel.

I think this is going to lead to a limit on the angular resolution θ

_{min} of about:

sin θ

_{min} = d/f = 1/N

One ultimate limit on the resolution is the rayleigh criterion.

sin θ

_{min} = 1.22 λ/d

where

θ

_{min} is the smallest angle it can resolve whatever the lens system

λ is the wavelength of the light you are using

d is the diameter of the aperture

This is coming from the fact that a hole will produce a diffraction pattern, the smaller the hole the wider the diffraction pattern. And if you do the calculus to find out when two diffraction patterns are indistinguishable it is 1.22λ/d

So the limit on sin θ

_{min} is going to be 1/N or 1.22 λ/d which ever is larger

Although I would have thought that taking photos at anywhere near the diffraction limit is going to be very very slow.