Common Mode Voltage. Although thermocouple signal are very small, much larger voltages often exist at the input to the measuring instrument. A typical example of an 'earthed' junction would be measuring the temperature of a hot water pipe with a non insulated thermocouple. If there are any poor earth connections a few volts may exist between the pipe and the earth of the measuring instrument. Common mode voltages can be minimised using the same cabling precautions outlined for noise, and also by using insulated thermocouples.
All thermocouples have some mass.
Heating this mass takes energy so will affect the temperature you are trying to measure. The first is that heat energy will travel up the thermocouple wire and dissipate to the atmosphere so reducing the temperature of the liquid around the wires. A similar problem can occur if the thermocouple is not sufficiently immersed in the liquid, due to the cooler ambient air temperature on the wires, thermal conduction may cause the thermocouple junction to be a different temperature to the liquid itself. In the above example a thermocouple with thinner wires may help, as it will cause a steeper gradient of temperature along the thermocouple wire at the junction between the liquid and ambient air. If thermocouples with thin wires are used, consideration must be paid to lead resistance.