I know from experience in the lab that ALL fridges have hot and cold spots (often +- 2-3 degrees), especially once you start putting objects in the way of the air flow...some fridges have better circulation than others...so placement of temperature measuring devices is very important...
As for the "accuracy" of any analogue measuring device, most are +/- 0.5 of the smallest increment...which makes most shop bought mercury thermometers to be between +/- 0.5-1 degree! I'd suspect the average stick-on to be +/- 1-2 degrees...
As for digital readouts that go to many decimal places, this does not necessarily make them any more accurate than your analogue type...
Then we get into the domain of method of measuring of the measuring device...an alcohol filled thermometr (red inside) and a mercury thermometer only read the same temperature at 0 and 100 degrees celsius. This is due to non-linear thermal expansion of both liquids...
So given all these sources of inaccuracy in measuring temperature, people should not be worried about a 1 or 2 degree difference, as the brew is possibly moving around by this much anyway!
The only true way of making sure you have constant and accurate temperature is to calibrate you temperature measuring device on a regular basis in the temperature range you require...not as easy as it sounds
I remember 1 experiment I ran, a temp fluctuation of 0.5 either way destroyed the reaction. Using a 1.5L glass reaction vessel, we could not get accurate and constant temperature throughout, so we got a 200L fish tank (i.e. huge thermal mass) and sank the reaction vessel in the middle
I'll stop rambling now LOL