I don't think analyzing for a few molecules is a viable approach at all.
In any lab, here will be a "noise floor", dependent on the quality of the lab procedures, and below that, you are likely to find loose molecules of any substance that was ever present in the lab, in any sample.
I agree. The more sensitive the test, the more likely you're going to get a false positive, just from ordinary contamination or cross-contamination, or test oversensitivity. I work with DNA and the biggest problem is that the lab air is filled with DNA from people and animals, and the sample has been in the air, which contaminates all the blanks immediately.
The second you crack the seal on the mother tincture, particles are floating around the lab, and no matter how many times you dilute, there's a good chance that particles will settle into the final dilution.
This will also be true of the blank controls, of course, so the key again is to be able to distinguish between diluted tincture versus controls, since both will have equal contamination.
Here's another thing: realistically, 'analyzing for molecules' is just the same as 'distinguishing between diluted tincture and control' anyway. Consider:
If we give the challenger a diluted tincture, it's in their best interest to just simply declare, even without actual testing, that they have found traces of mother tincture. We will spend further time haggling over whether the test was done, whether it was done properly, &c. We will need to open the lid and understand the test.
In order to protect against this, we can also give them blinded controls. Which is to say, we need them to distinguish between samples and controls, and we're back where we started with JREF's official homeopathy test policy anyway. At this point, what's the point of this thread?