Is it possible to achieve arbitrary precision to the calibration of the extrinsic parameters of a camera or is there a minimum error wich can not be compensated (probably dictated by the camera's resolution)?
It is not possible to achieve arbitrary precision in camera calibration, precisely because of camera resolution and camera imperfections (e.g. lens distortion, which is only approximated in the calibration of intrinsic parameters).
That, however, isn't usually the worst part of the deal. You can go a long way if you are able to fabricate your calibration target with a decent precision. According to Trucco (p.124):
The accuracy of calibration depends on the accuracy of the measurements of the calibration pattern; that is, its construction tolerances. To be on the safe side, the calibration pattern should be built with tolerances one or two order of magnitudes smaller than the desired accuracy of calibration. For example, if the desired accuracy of calibration is 0.1mm, the calibration pattern should be built with tolerances smaller than 0.01mm.
A good quote for common sense, also by Trucco (p.136):
A practical guideline is: the effort going into improving calibration accuracy should be commensurate to the requirements of the application.
 E. Trucco, A. Verri. Introductory Techniques for 3-D Computer Vision. Prentice Hall, 1998