Audio Amplifier using an Op-Amp
This is an inverting amplifier with a mid-band gain of \$\mathrm{A_v=-10k/500=-20V/V}\$. Since this is an inverting amplifier, beats may be heard a bit odd because the push of a beat turns into a pull (think of the movement of the speaker's outer cone).
C424-R2 pair brings a high-cut at \$\mathrm{f_c=(2\pi \ 10k\ 80p)^{-1}\approx199kHz}\$, which is way beyond the audible top-end limit but shouldn't be a problem here.
And R3-C118 pair brings a low-cut at \$\mathrm{f_c=(2\pi \ 33\ 100\mu)^{-1}\approx48Hz}\$. We might expect this to be under 20Hz but the headphone may not be able to generate sound (e.g. sound muddy) at those low frequencies. So 48-50Hz seems acceptable.
So, the output signal (at pin-7 of the chip) will be 20 times the input signal (i.e. 8Vpp = 2.8Vrms). Assuming the headphone's impedance is 32 Ohms, the output power will be Pout=2.8² / 64 = 0.12W, and half of this power (~60mW, a reasonable value) will be transferred to the headphone. So, no problems in terms of electronics design.

I hear small salt-and-pepper type noise in the audio.

Maybe you should check the wiring and setup (i.e. supply, decoupling capacitors, etc.). If you post a photo of the setup in the question then it'll be easier to help.