What are the challenges of designing high Q digital filters?
High Q filters, have poles very close to imaginary axis (unit circle for digital filters). When implemented on a digital platform, the truncation errors introduced in the coefficients can push the poles of the filter to the right had side plane (outside unit circle for digital filters). The resulting filter is unstable. Passive, analogue filters won't have this problem.
Another problem occurs if the gain is very high; Arithmetic overflow can occur in the internal states / variables.
Even if it doesn't overflow, adding large signals with small signals can cause the addition to be ineffective if both the numbers vary by large orders of magnitude. Link 1
With floating point arithmetic (and enough number of bits) this may be very unlikely to happen and can anyway be tested before deployment.