I have a setup similar to this one: amp, 100uF cap leading to headphones, nothing more. Powered from a Pi-Ion battery @3.9V.
It had worked fine with MAX4466, but after replacing that with MAX9814, I get VERY loud high-pitched noise. The mic is responsive, and the noise even dies for a fraction of a second when I am providing it with very loud sounds myself (like tapping the mic)
The noise appears to be feedback from the (very small) 32 ohm Philips headphone speaker:
Moving the speaker closer and further from the module changes the noise frequency (Doppler effect) Works even at 80cm (my cables don't reach further).
 Tried different headphones, 140cm away - same.
Dropping max gain from the default 60dB to 50dB makes is a little better (until the autogain gets there again) and at 40dB makes the noise cease at distances over 20cm. Similar with a pair of Panasonic headphones (not disassembled), but there, noise can disappear at over 35cm at 50dB. At 60dB, still appears at 140cm.
Granted, the module was purchased from ebay not from adafruit, but the board design appears to be the same.
The question, again. is whether all that is perfectly normal, or not.
The fact I have not read about it on the sites which decribe how to connect a headphone jack to the MAX9814, on the default gain setting, no less, leads me to expect it is not. The effect happens with the (Panasonic) headphones a full cable length away, after all.