What's the smallest size a human eye can see?
Very nice question!

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:

 

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 &amp; Luu). 

Using the basic structure of the eye and some trigonometry one can deduce the smallest visible size :



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).  

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. 

A young child can focus at distances down to ~50 mm, and can have a visual acuity of 0.4 MAR, which yields 6 microns. 

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.

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. 

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