[southern_cross]

If you've read a few of the relevant papers and reports like I have, then you would know that they routinely state that they assume that most of the errors and uncertainties and such cancel out. But mathematically you can't get away with that; instead you have to know that they mostly cancel out, using whatever methods legitimately allow you to know this. But since we only have really good instrumentation and data going back at most a few decades, there's no way they can actually do that (at least for most of the historical data), so instead they just pretend.

And to my point, no, you can't claim that the errors in various temperature readings mostly cancel each other out, without having any solid proof of that. Nor can you then turn around and claim that since there are enough errors out there that obviously don't cancel out, that this then gives you the right to set loose a computer program to blindly "correct" those errors, said program having been constructed using whatever models and biases you were operating under at the time. (Those "corrections" may not be anywhere close to accurate, in other words.) But that's exactly the kind of thing they've been doing.