three stage amplifier
To mention an obvious disadvantage, LMC7111, that's used in the circuit, has a GBW (gain bandwidth product) of 50 kHz, so the amplifier bandwidth with gain of 1000 is about 50 Hz. Most likely less than intended.
It's no problem to achieve a gain of 1000 in a single stage with an appropriate fast audio OP. (But 1000 is typically too high for a microphone amplifier).
You shouldn't use however fast OPs in breadboard design without any bypass caps, as presented in the link.