Finished films contain visible continuity mistakes, including in productions with substantial budgets and dedicated continuity staff. Most of them were noticed and kept deliberately.
The choice is between two defects
An editor assembling a scene picks from takes that differ in performance and in physical detail, and those two qualities are not correlated.
The strongest delivery of a line frequently comes from a take where a hand was in the wrong position or a glass held a different amount.
Choosing the matching take means using a weaker performance, and a weaker performance damages a scene more reliably than an inconsistent prop does.
Audience attention is directed, not distributed
Viewers watch faces and follow dialogue, and their attention is guided by composition and by the cut. Peripheral detail is processed loosely.
Errors sitting outside that focus commonly go unnoticed on first viewing, and a film is designed for first viewing at speed rather than for frame-by-frame inspection.
Editors judge accordingly, weighing whether an error falls where attention is or where it is not.
Some mismatches cannot be avoided at all
Coverage shot on different days brings different weather, different light and sometimes visible differences in a performer's appearance.
Reshoots months later create the same problem at a larger scale, and no amount of on-set discipline resolves a gap that was created afterwards.
Grading and visual effects fix some of it and cannot fix all of it, particularly anything involving physical position or the state of an object.
Continuity's real job is preventing the unfixable
The department exists to stop errors that would make footage unusable, such as a character wearing the wrong costume for the story's timeline.
Those mistakes remove options from the edit entirely, while a glass at a different level merely costs a small inconsistency.
The role is therefore triage rather than perfection, protecting the errors that cannot be traded away and accepting the ones that can.
Why the errors get found later anyway
Home viewing allows pausing, rewinding and frame-stepping, which is a viewing condition no film is edited for.
Catalogues of continuity errors are largely a product of that capability rather than evidence that older productions were less careful.
Knowing the audience will eventually inspect the film this way changes nothing about the trade, because the alternative is still a worse performance on every ordinary viewing.