"Earth Loops would not be an issue
This fact is not totally accepted until it is realized that Earth is not always derived from Terra Firma (as in 'Ground'). It is often derived from the Neutral which is grounded at the transformer only. If the Earth is derived from Neutral (usually at the meter point or switchboard) then it takes on the voltage of Neutral which is not 0V as the cables have resistance. Earth is therefore better regarded as a Safety Earth, and not a reference to true Earth or Ground.
The fact that the Safety Earth is related to Neutral is not in itself a problem. It is when pieces of equipment are connected to each other as a system and spread over an area or across distributed mains supplies, then any disparities between the earth voltages will manifest as currents especially along the "signal ground" lines or coax shields. The voltage difference and the impedance of the signal ground will determine whether the earth loop current is merely a few mA or many amps.
Those who remember older pieces of computer equipment will also remember that the frame or chassis was never connected to either mains earth or the circuits. This allowed the installation specialist to determine the best method of earthing the device and, even if he fouled up, the chances of creating an earth loop were pretty close to nonexistent.
The problem with modern equipment is, in order to keep costs down, interface sockets are now mounted on printed circuit boards and for (stupid) health and safety reasons the mains earth is taken back to the signal ground. Any ground loop currents now manage to find their way through the printed circuit board which was designed by an inexperienced individual with no such currents borne in mind. These currents, through magnetic coupling, can influencing the circuitry itself. Currents of a few mA usually don't cause much of an issue, but then "few" is a relative term!
Disregarding the current, this earth/ground differential voltage is also summed with the audio or data signals, and depending on the level can be either construed as noise or signal. The real challenge is when it is on the border of noise and signal and, under the right circumstances, crosses this border every so often. The results can be anything from an obscure character on a screen full of data, through to a system crash.
Such a voltage may not actually cause a problem. An example is a telecomms circuit with a frequency range of 300-3400Hz (with pretty sharp filters). 50/60Hz falls well below this and may be so attenuated it is not regarded as interference. However, the problem is the voltage is not necessarily made up of a fundamental 50/60Hz, but also made up of a high harmonic content and/or noise as a result of various non-linear loads and switching equipment, and such signals fall within the bandwidth.
Balanced signalling systems were designed to combat this, but there is one other issue not often thought about - even amongst those who are supposed to be "in the know". Such signalling systems are usually capable of a maximum "common mode" input range, and if the voltage exceeds this range the inputs "clip" or "saturate" and cause modulated signals or corrupted data.
There is also the problem that such balanced circuits are not quite balanced (i.e. each input line has a slightly different input impedance or gain) and the common-mode voltage is not fully cancelled by the balanced input. This is more pronounced in audio circuitry such as sensitive microphone inputs, especially phantom powered where the shield is used as one leg of the supply. More of this later.
We have split the various interferences mentioned into analogue and digital (i.e. sound and computers).