Earlier quoted context omitted.
The Central Limit Theorem smooths any errors. Decades of observation data make instrument errors very easy to spot. In recent decades daily MODIS (satellite) polar orbit overpasses provide air column and ground temp data that infills station data (from 1900 onwards). There's a science to ground truthing, error detection, and data correction. Here's the gross single number continent wide average over a century: http:/…
Only sometimes. It is easier to measure in cities, and thus introduce bias based on whatever pavement is populate. There is a lot of data, and the people who measure this (or at least some of them) are aware of the issues and so correct for them. However you cannot just blindly apply the central limit theorem.
Apart from yourself, implying that happens as a matter of course?