The bilinear transform, line any other discretization method, is an approximation, so we will introduce some errors. The size of that errors are related to the sampling frequency since a very (very very) high sampling frequency, in some cases, could seem continuous. In real systems, where the sampling frequency depends of the ADC and many real components, we can use high sampling frequences, but in other cases we will introduce a significantly error.
In case of the bilinear transform, one of the errors that we will introduce is the frequency warping. This effect produces a shift of the natural frequency of the filter. This effect may be negligible in the case of a low pass filter, but in case of narrow band filters, the error could make that the filter don’t work.
In order to find the error caused by the bilinear transformation, we need to find the relation between the analog frequency and the discrete frequency.