That is a 100 Ohm. It is just to zero the meter. The value is not important aslong as you have enough room to zero it over the whole frequency range and it is not so big so you can not get it to precise zero because the range becomes to big and turning it to coarse.
If you fix the meter at one frequency then something around 40-50 KHz is a good value. ( remember this one measures ESR and not |Z| so there is no need for 100 kHz, the ESR difference between 50 and 100 kHz is small and paracitic effects ( like ESL) are smaller at lower frequency. And if you allways use the same testleads you can use the 100 Ohm trimpot. If you use longer and shorter leads use a potentiometer on the frontpanel. 1K is a nice value
If you do not get a 50 % dutycycle with the inverters, try some differents makes/years. They turn out to be rather unpredictable in performance. You can replace then by a 4013 and wire it accoording the datasheet for divide by 2 and use Q high and Q low outputs. The frequency of the LM339 oscillator needs to be doubled in that case. Just play around with the RC values. It can oscillate over a huge range. Mine does 20k to 200 kHz and after the 4013 it is 10-100 kHz. But that is only for "research" and experiments reasons. If you just need an ESR meter for repair then fix the frequency.
I first used the 10 K resistor and 100 Ohm potmeter ( mounted on the front) but later a 10K, 1 K multiturn and then a 1K potmeter. This because I use 1 meter long kelvin testleads and a 100 kHz span..
The zero offset is changing over frequency ( things like skineffect) so I set the frontpanel potmeter in the 50 % position. Then adjust frequency to 50 KHz and use the multiturn trimmer to zero. Then I check if I can zero with my 4 long testleads over the whole range. If not I use both to find the position that makes it possible to zero it over the whole range. In my case the potmeter is allmost max ccw at 10 kHz and allmost CW at 100 kHz. With a test fixture ( to copper planes to press a capacitor on and two clamps to fix the capacitor pins, bridged by a shorting switch) straight on the banana sockets it needs much less adjustment and you can use a smaller potentiometer if you like.
Version 5 is now in design. The squarewave will be made by a uP, that will control 2 very fast analog swiches ( better performance as the 4066) the DVM will be replaced by the 12 bit ADC that also performs the zero. It will also get an automated DC leakage test and reform function. ( if we get that to work) it must increase the testvoltage upto a variable maximum over a free to choose time and monitor leakage, each time leakage is dropped under a limmit the voltage will be increased. If the leakage stays to long above that limmit it aborts reforming. So you can leave it without the danger of exploding caps.