Is it normal to have this much fluctuation in an RTD measurment in boiling liquid?
That's a pretty mediocre chip to be expecting 0.1°F stability from. At 1mA 0.1°F is about 8uV. The chip has typical noise of 150uV over the bandwidth, and thermal EMFs can cause errors of some uV here and there with little trouble.
If you are running the probe at high current you might also be getting variation from bubbles and heat loss, but less from the noise and air currents. Depending on construction self-heating will be an issue even at 1mA when you are looking for +/-0.055°C.
Your reference resistor should be a precision type 25ppm/°C or better.
If you have a reasonably good digital multimeter (preferably 4-wire) you can just hook it directly across the sensor (remove the other circuitry, obviously) and confirm one way or the other.