So when you measure isotope what do you use? What type of device or instrument?For paleoclimates they measure an isotope of oxygen found in ice cores. The prevalence of that isotope is indicative of a corresponding temperature. The interesting thing is that as CO2 concentrations in ice cores rise so does the temperature as measured by the oxygen isotope. So we can see a direct relationship between CO2 levels and temperature increases and decreases over the last 800,000 years.
Today temperatures are measured with typical weather instrumentation, thermometers and satellite imagery. Global average temperatures today are the highest since modern records have been kept (the last 150 or so years). One degree F doesn't seem like a lot for any one particular area, but for a global average it is significant as the Earth usually does a pretty good job at keeping a balance. The thing concerning the majority of climate scientists is the trend doesn't appear to be abating. The computer models indicate if the current trend continues that by the end of this century we could see as much as a 7 degree F rise in temps (worst case scenario).
Typical weather instruments have an error factor of what?