Decreasing manufacturing variance in analogue designs
Do a sensitivity analysis of each component in your circuit. Pt100 DIN changes about 0.385% per °C, so a 3°C error represents ~1% overall error. This will also inform your selection of components for stability with temperature, moisture, time and soldering. In this particular case, resistor tempco should certainly be considered for the critical parts. 1% tolerance does not necessarily mean they are extremely stable with temperature.  

Errors can come from resistor tolerances, errors in the nominal resistance values when mapped to standard values (can be reduced by using series or parallel arrangements of standard values), amplifier offsets and bias currents, reference voltage error and so on. 

A couple of calibration trimpots (span and zero) can cancel out many different sources of errors at once, or more suited to modern times, if you have the numbers in a microcontroller you can apply digital scale and offset values for calibration, and even correct for linearity and ambient temperature effects.