Expected repeatability of PT100 temperature sensor
If you are putting 1mA thru the PT100 you might get a little bit of self-heating error. 1mA into 100 ohms (0degC) produces a power of 100 uW - not much of course but you are asking about errors in your question.

You might also get spurious thermocouple errors due to dissimilar metals making contact and being heated at different temperatures. It's hard to rule out anything in this area and typically a k type thermocouple produces 41 uV per degC so, some random dissimilar-metal connection might be one-tenth of this and, if at some elevated temperature compared to the rest of the system could produce errors of a few hundred micro volts.

Regards noise - it's a resistor and behaves like any other resistor re thermal noise BUT, mechanically it's more like a strain gauge and therefore mechanical stress can affect its reading.