A question I have is whether you are actually interested, or if you merely pretending interest, Indeed, if you're actually interested, there is a lot of work being done in analyzing data and comparing data from different times, which is (as you imply) indeed not always trivial. And there is a "damned if you do, damned if you don't" problem for the people doing the actual work, of course, because if they don't correct the data errors, they're criticized for not correcting them, and if they do, they're criticize for "adjusting" the data. They deal with this by being very transparent in how they analyze the data, which is extensively documented.
The first thing to know is not the sensitivity of the thermometer, though; it is the statistics of measurement. I do assume you're aware that a large number of measurements is more precise than a single measurement, right? So the first question you should be asking is, how many measurements are being incorporated into each statistical data point. Ten thousand measurements with a precision of 1 degree, for example, give an average with a precision of 0.01 degrees. Good introductions to statistics of data analysis are available many places, including on the web, for example:
https://www.princeton.edu/~cap/AEESP_Statchap_Peters.pdf or somewhat more detailed,
Moving in to measurements: there are four main institutions that are doing the reconstruction of long-term temperature measurements; most of your questions about thermometry are answered by citations in the references of the papers they publish on their technique. It does take some work to dig down through the references, though. If you want to start, most of the recent papers are online. I would start with the Goddard Institute of Space Studies papers. The full list is here:
The two papers you should probably start with are Hansen and Lebedeff 1987,
and Hansen et al 2010:
If you don't want to dive that deep, there are some review papers that cover most of the material you're interested in. The Berkeley Earth Surface Temperature project has a couple of good top-level papers, with an overview:
and a paper on data quality: