SZ-31MR video sound recording issues?
The constant chatter of the AF would be picked up by the microphones, and the camera is designed to mute the sound, and filter out the high frequencies when internal noises (particularly the zooming) are picked up.
On my SZ-30MR, drums and clashing of sticks cause muting and low-pass filtering to persist. The almost constant muting, low-pass filtering and excessively critical picking up of internal noises on your camera could indicate it is faulty.
Try resetting the camera first. If the problem persists take it to the shop.
The two microphones are above the lens under the flip-up flash.
I have the very similar SZ-30MR, and I never had the problems you describe. My last camera that picked up focussing chatter was the C-750UZ from 2003.