The only effects likely to ensue from poor mains waveform fidelity etc are on mains synchronous motors such as those often used in turntables, and in very bad cases in producing mechanical buzzes etc directly from transformers. The latter can be annoying if loud enough and in a quiet enough environment of course! Unlikely to effect sound though.
In a motor powered directly from noisy mains the actual rotation of the motor shaft will be modulated by the mains noise and distortion which will result in extra mechanical noise etc from the motor... not good.
Virtually everything else in a hi fi system converts AC to DC before using the power and this process is pretty much immune from mains issues. Most items will also use voltage regulation which removes all changes in the actual voltage level ie if the mains was varying between 230 and 248 volts it would make no difference whatsoever to the output of lets say a 15V regulator in a pre or CD player. It will stay at precisely 15V as it is designed to.
I could easily design and build a mains regenerator for my own use from surplus parts for very little money but the fact that I choose not to shows the importance I attach to this issue
RFI from the mains, from speaker cable and other sources can be an issue and the sensitivity of equipment to this will vary VASTLY between different pieces of kit. One amp may be 1000 times more likely to be effected than another. This has nothing to do with the mains itself or special wires etc though! You could have a fantastic mains regenerator and then pick it up just the same in 20' of cable between it and the hi fi.... speaker leads are more important in this respect as the RFI is going straight into the power amps output.
The fairly sudden ubiquitousness of wi-fi is a major problem here, as are mobile phones, and the RFI can get in through even small gaps in casework etc. Most good quality RF gear for VHF and above is built in boxes with a fixing screw maybe every 1/2" which seems totally OTT until you realise it has nothing to do with the mechanical strength of the box! Fine wire mesh will also be used over ventilation holes etc for the same reason