And if the ADC doesn't have any sample-and-hold circuit, then you may get very, very strange readings if the ADC conversion is slow and teh input voltage changes during the measure. If the ADC converts a single bit at a time, it isn't too good if the first bit (the most significant) suddenly is wrong because the input signal has moved past the threshold for the bit.


Nyquist shouldn't be ignored, but if you don't care about recreating the wave form, then you don't have to consider twice the input bandwidth. If you know that the input signal is very close to 50Hz or 60Hz, then you can sample at a lower rate and then compute a best-fitting sine wave. Web pages describing the Nyquist theorem normally shows how you measure a false, much lower, frequency because of aliasing. But in the case of measuring the mains voltage (and assuming no distortion) you don't need to bother that the measurements may indicate a 10Hz input signal. As long as your sampling rate isn't close to 50Hz/n or 60Hz/n, you can sample at a way lower frequency (while having to wait longer for enough measurement points). But there must be drift (or randomnes) between your samples and the input frequency, so you don't manage to sample every fifth zero crossing or similar.

Creating a precision power meter, on the other hand, will require a quite high sampling rate since it isn't enough to figure out a single amplitude - you may need to capture a signal bandwidth of > 10kHz to get a correct power factor when there are distortion or very ugly high crest-factor currents. This obviously also requires a lot of bits of resolution from the ADC.