It would help us be clear about exactly what objects you are referring to if you labeled the false positives. Do you mean the dark regions which look to my eye like background (like x=150, y=480), yet other regions that are dim, but apparently inside the cytoplasm (region around x=260,y=220). Assuming I have the right idea, I would try these:
(1) Raise the “Threshold correction factor” incrementally. Apparently you have lowered it to 0.6 for some good reason, though, so this may create some false negatives.
(2) Try 3-class Otsu. This is the setting right below where Otsu is chosen. Since the foreground has a fairly high variance (some bright speckles & lines, as well as some dim, yet still positive(?) cytoplasm areas), you can then “Assign pixels in the middle intensity class” to Foreground. I would start with Global thresholding, since adaptive can sometimes get too liberal in calling foreground, especially in dim regions.
If this does not help, please post the actual pipeline and an example image.