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Hence, visual acuity has to be measured as a function of viewing distance, i.e, in degrees of visual view. Measured in degrees, the visual acuity of the average normally sighted person is 1/60 degree, or 1 minute of arc (1 MAR) (Webvision, chapter "Visual Acuity", by Kalloniatis & Luu).

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During a biology experiment at school, where we would look at waterweeds under a microscope, my teacher said something about that it's impossible for the human eye to see the cells without a magnifying glass of some sort. So, I saw that as a challenge, and decided to check if I could see the cells. And after holding the leaves really close to my face, I was indeed able to see tiny rectangles.

So, I wondered, what is the smallest size a human eye can actually see? According to a whole bunch of sources all across the internet, it's either 200-400µm, 100µm, or 58-75µm. I also hear 'the width of a human hair' very often, but those can range from 17 to 181µm.

The trigonometric formula becomes: $2d \times tan(\frac{\alpha}{2})$ with d being the viewing distance and alpha ($\alpha$) the visual acuity expressed in radians ($\pi \times \frac{degrees}{180}$) (NDT resource center).

PS - the values described are representative under ideal conditions, i.e., under situations of abundant lighting and high contrast.

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Since I was curious about it now, I decided to look some more things up. First, I tried to find out the actual size of waterweed cells. Based on this 640x enlarged image, which features cells of 5mm wide and 10 - 15mm long in the picture (which corresponds with of roughly 8µm wide and 15µm long).

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I left this in the back of my head for a long time then, but I just looked at my cotton sleeve, and noticed tiny fibers. Not the ones that are woven together, but ones that are standing out from it. So, after looking it up, it turns out that cotton fibers are 10 µm wide.

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First of all, the 'smallest size' that a human eye can perceive is called visual acuity, and can be expressed in various ways. It cannot simply be expressed by means of size measures, as objects with a fixed size are perceived as smaller when viewed from a distance (perspective). A familiar example is the train track:

Assuming the closest distance an adult can focus (~100 mm) and an average maximal acuity of 1 MAR, the smallest visible size boils down to 29 microns.

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Note that 1 MAR encompasses 288 microns on the retina, and some 180 photoreceptors. The optical limitations of the eye (such as diffraction by the lens and light scatter by the neural cells in the retina) limits the resolution of the human eye below the theoretical 'pixel limit' of the eye.

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So to sum up, depending on one's age, one should be able to see targets in the order of 6 - 29 microns. The lower bounds of this range are indeed in the range of the waterweed cells and cloth fibers you describe.