You'd have to ask The Internet on methodology. The studies/papers I've read on the subject take most of these concerns into account. They don't ignore them because it would as you've pointed out create a realistic problem.
Statistically speaking...your margin of error for prior measurements would be higher...just on numbers alone. The accuracy of measurements to form an average would then produce some level of certainty in the average. When comparing temperature changes between years/decades/centuries...you would do a statistical test against those errors to make sure that you were within the range of statistical probability and your power was sufficient. You'd have to make sure that your power allowed you to obtain the correct confidence interval to make the discrimination between the two averages.
Again though, I think most studies cover that, but The Internet might be able to provide more insight on the issue.