Strings of LED's

The image below is from an electronics magazine.  The circuit is designed to light a string of LEDs (Light Emitting Diodes) to indicate the intensity of an audio signal presented at "INPUT." The combination of the diode and C1 form a peak detector.   As the amplitude of the input increases more of the LED's should light up (i.e., D23 lights for even a small input, but D28 won't light up until the signal gets very large). All of the diodes are standard Silicon diodes (i.e., not ideal) except for the bottom ones (D23-D28), which are LEDs .  For our purposes, assume the LEDs have current-voltage characteristics like the other diodes, but emit light when current (>1mA) flows through them.  You can use either the constant drop model or the exponential model of a diode (the ideal model is not useful in this case).

Can you explain in two or three sentences (note) why it doesn't work.  Can you think of an easy fix?