In spite of more important things to do, I spent some time on measuring Zin. My high school physics teacher, Mr. Peterson would say "how do we know that g is 9.8 m/sec^2? We measure it!"
To do so, I set up a Fairchild uA339PC on a breadboard. I biased pin 6 (-input) to half of VCC (5 V) with a voltage divider of two 10K resistors. Relative to that, I applied a 1 kHz sine wave of various amplitudes to pin 7 (+input) through a 1M0 resistor. I used a Tek TX3 4.5 digit DMM to monitor the voltage after after the resistor both unloaded and loaded. I then determined the value of Zin with simple algebra. Note, the TX3 has an input impedance of 10 Mohm in parallel with approximately 100 pF. I neglected the capacitance and did not treat the meter as a complex impedance in the calculations. I've attached a graph of the results.
Based on one sample, it appears that the LM339 has a differential input impedance in the 10's of megohms for inputs between 25 mV and 2 V RMS. Above 2 V, I would expect to see a reduced impedance as the LM339 inputs are driven beyond their specified range. The reduction of impedance at levels of 25 and 50 mV is probably due to noise. Even though the breadboard and meter are on a metal panel connected to the circuit common, there is noise induced, most likely from the function generator and power supply that are in a stack and not as close as I would like. If there's enough interest, I could revisit the setup and properly isolate the drive and also isolate the meter loading from the circuit.
I also tested the bias current as a function of common mode and differential voltage. The TX3 has a resolution of 0.01 uA or 10 nA on its most sensitive range. This makes reading 50 to 100 nA somewhat problematic. However, in spite of a 20 - 30 nA bobble in the reading, I did not see a material change in the +input bias current as I varied both inputs from about 0 to 3 V. It dropped off above that. I also didn't see a material change when setting the -input to 2.00 V and varying the +input from 0 to 3.5 V.
This makes sense given the design of the input stage. Refering to the simplified schematic posted above, Q1 & Q4 are PNP emitter followers with their emitters biased to V+ with separate current sources. Neglecting the diff amp Q2 & Q3 for the time being, the base currents of Q1 & Q4 must be 3.5 uA dvided by their respective HFEs. This applies for base voltages greater than when their base-collector junctions are forward biased and less than when there is insufficient voltage across the current source for it to operate.
Bringing the diff amp Q2 & Q3 back in, the common emitters are biased to V+ with a 100uA current source. Depending on the relationship between the input voltages, the base currents of Q2 & Q3 can vary from 0 to 100 uA / HFE. If the HFE is 100, the bias current to the emitter followers can vary by 1 uA from 3.5 to 4.5 uA. This will manifest as a variation in the input bias currents but I can't see it with my setup. It would be nice to have a more sensitive meter. Anyone got a VNA that will work at low frequencies?
Anyway, the bottom line is that as long as the inputs are operated within their limits, the bias current is fairly constant and the input impedance is quite high for a bipolar input device. The emitter followers are doing a good job of buffering the input pins from the differential amplifier. Also, looking at the graph, Zin actually seems to increase as the differential input voltage increase. I suspect this is due to the differential amplifier transistors alternately being biased off and not contributing base current to the emitter follower stages.