The relationship between the physical quantity and the raw analog signal is often linear. This is convenient, but it may not necessarily be the case; it could be almost anything; polynomial, exponential, logarithmic, etc.
For a useful instrument, the relationship between the input and the output must be known over the range of interest.
The most important goal of the processing stage is essentially to compute the inverse function of the transducer.
How fine is the measurement? This should be scale independent; it is generally expressed as percentage or number of significant figures. The is a fundamental limit imposed by the nature of quantity being measured. All continuous quantities have some amount of uncertainly associated with them. For example, it is not possible to measure the distance from Ann Arbor to Helsinki in millimeters; the locations or boundaries of those cities are not specified that precisely.
How closely does the indicated value conforms to the true value? It is never possible to measure a continuous quantity to an arbitrarily high precision with zero error. The exact value of the error is unknowable (otherwise you could subtract it from the measured value to cancel it). One can often make an upper bound estimate on the error with good confidence.
There are several types of errors:
Rising and falling curves of transducer do not overlap. Area bounded by the curves is a measure of the amount of hysteresis. Any system that stores energy has some hysteresis. This is a fundamental consequence of the second law of thermodynamics; any process that transports energy is never entirely reversible.
Circuitry attached to any analog transducer to measure the output value will affect that value.