A good guide to using QGIS for orthorectifying images and, at the same time, assessing the errors can be found here:
Orthorectification of a large dataset of historical aerial images: procedure and precision assessment in an open source environment
Like any operation which involves measurement and processing, orthorectification implies uncertainties, which are important to be quantified in order to give a valid assessment of the output.
Generally speaking, to improve the accuracy of your orthorectification process, you want to have:
- more GCPs; this ensures tighter control and better statistical distribution, resulting into lower sigmas and lower average residuals.
- better GCPs coverage (i.e. GCPs which are more homogeneously distributed)
- better border coverage (i.e. GCPs at or near the borders of the original image). This avoids areas with overly extrapolated parameters.