...but nothing after the diode.
...The "nothing after the diode" means the scope registers nada here....
[Place a radio or so in front of the microphone and measure the DC voltage after the diode.
If you are interested in db, have a look at the AD8307 (Analog Devices) - it is a logarithmic amplifier which gives you 0.0-2.5V DC output (for your ADC) when the input signal is -80..+12dB (90dB range). It is a DIL8 chip, you need 1 resistor and ~3 capacitors and you get a calibrated db voltmeter.
Update: * The "nothing after the diode" means the scope registers nada here. I haven't actually attached the Arduino yet.
I'm getting a nice amplified signal on my scope from pin 5 of the LM386, but nothing after the diode.