Several thoughts ..
(a) errors are an inescapable consequence of that which we do so we, as pilots, engineers, whatever .... need to put sensible error trapping routines in place to minimise and mitigate both the errors and the magnitude of their consequences.
(b) I suggest that, overall, errors in pax ops will be more routine but of lesser magnitude than in freight ops due to the use of standard weights versus routinely running the can over a weighbridge ... but be very wary of bridge problems and errors.
(c) the loading system designer (of which I am one) routinely does, or should, build in some conservative fat to the system CG limits to account for reasonable error analysis considerations ... this involves a reasonable review of the operation's realities.
.. and, at the end of the day (or night) when it all turns to custard .. we rely on the driver to save the day. This is one reason why severe misloaded takeoffs ought to be an occasional sim exercise ... to allow the pilot to get a feel for the very unusual stick loads etc ...