In the plot of temperature of the global warming, the measurements start from 1860. How was the global temperature measured at that time? How accurate was the measurement?
In 1860 global temperature was pretty much measured the same way it is now, with thermometers.
In 1860 thermometers were the standard mercury filled thermometers we still use today. The accuracy of each individual measurement was very close to the accuracy that you get nowadays with the exception of the fact that thermometers were not as accurately calibrated as they are today. The latest calibration scales were put into effect in 1990. Prior to that the margin of error was slightly higher but not to the point that data before this is not valid.
Considering modern equipment that is much easier to use and can be monitored remotely are still checked weekly against a mercury thermometer, we can assume that mercury thermometers are very accurate.
Unfortunately in 1860 there was not nearly as many data points as compared to now. That does decrease the accuracy of the data when you are considering you have to average them for the whole planet in order to determine a heating or cooling trend.