You mean the 3.3uF just before the diode? I didn't know I needed a discharge path for it. How should it be? Do you want me to turn it into an HPF? Because I tried that with HPF 0.48 Hz and it doesn't get rid of the noise.

Yes, the diode will charge up the capacitor. You don't show a pull up or pull down resistor on the input of the micro. When the capacitor gets charged up, you will have a DC offset on the output, because there is no way to discharge the capacitor.
Exactly, how are you proposing the measure the output of this system?

 

The circuit has a voltage gain of 200 times. Then an unshielded input cable and wires all over the place on a breadboard will pickup all kinds of interference noises.