How accurate they are depends on how consistent the capillary diameter is and how accurately the markings are placed on it. I bet you can find Chinese shit-tier mercury thermometers that are worse than the outdoor dial-style plastic thermometers. And nobody's calibrating a good thermocouple with a mercury thermometer because that's just stupid when you can use an ice bath and be far more accurate.
We did exactly that. The mercury thermometer, one not made in China because that's stupid, was used to measure the exact temperature of an ice bath to calibrate thermocouples and one-wire devices. We had RTDs as well, but those were primarily hot so there was a calibrated oven for that job.
An ice bath is only as good as the circulation and pack of ice in it. You can still have localized spots that are a slightly different temperature.
So how do you tell on the mercury thermometer whether the ice bath is 32.01°F or 32.07°F?
For our purposes, the 1/4 degree graduations on the mercury thermometer are sufficient. If further accuracy is required - and the thermocouple readers we use don't require it - we have NIST-traceable calibrated digital units that are accurate to 0.01°, but we rarely care about more than 0.1°. At those levels, unless you have a >16bit A/D in your reader, you're getting into dither.
I did check and see what is in the cal drawer, they've purchased a 0.1° unit since I've been away.
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