Question: Is it possible that the socket orientation (in Europe: one pin 230V, the other ground) can have an effect (albeit very small) on the amplifier behavior of a very old stereo sound system? What is, if any, the underlying reason ?

Answer: 
I can think in one effect but only for a very specific hardware. If You're using a [capacitive supply](http://electroschematics.com/5678/capacitor-power-supply/) with a [half-wave rectifier](http://en.wikipedia.org/wiki/Rectifier#Half-wave_rectification) - In this case the circuit ground is connected directly at one of the socket pins. If this pin is the ground its ok. If this is the 220 AC, although the circuit still operates, you may have some noise coupled on the circuit via ground, as your new ground is oscilating at 60Hz with a amplitude of 220 volts
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I would imagine this could introduce some unexpected ground loops and so increase both hum and noise levels. - especially if the amp is connected to other kit with hot (live) and neutral (connected to ground/earth) wired the other way round.