Rounding and precision issues can be very significant in digital signal processing.
For example I inherited an IIR filter in a control application and eventually realized how poorly configured it was for the task. Small signals (and as an error amplifier that's all it should see) multiplied by small coefficients rounded to zero, essentially negating that coefficient and meaning that the transfer function/step response varied significantly with signal amplitude.
The solution was to add additional fractional bits. But with fixed point math and/or large dynamic range in coefficient values these problems can be very significant. It's very important to evaluate real life performance which simulate the constraints of the real system.