I did wonder what the purpose of R3 was. It seems like it would limit the current dramatically with any kind of load at the amplifier connected to it. If it does do that, it would probably cause the supply rails to go all over the place and sag lots.
Wouldn't the current limit, noise and a whole load of other specs of that opamp also affect things? For example, if the output of that opamp is noisy, that noise is then on your virtual ground, and since the rails are referenced to ground, the rails will be noisy? Then that noise, if of a high enough frequency / poor decoupling might make its way on to the actual amplifier output?
Then the current limit. Apparently it's 20mA for the 741. Doesn't all current have to return through ground? So would that limit the actual amplifiers current to 20mA, even if the output opamp is rated for [extreme example] 500mA? This would cause clipping if the load was nasty enough. If R3 does limit the current, surely this would just make matters a whole lot worse? Perhaps if it was a really low value, like 4.7R or something, but then I am still not sure what purpose it would have? To isolate ground from something possibly?
Some opamps do apparently need a resistor in the feedback loop with unity gain, but such a high value resistor shouldn't be in series with the output of this opamp I am sure.
Could this be the cause of the hiss you are hearing?
I'm quite curious, so if someone who knows could explain it to me, I would be grateful! I'm largely guessing.