Answer: ciliated epithelial cells and detached ciliary tufts (ciliocytophthoria)
This case demonstrates a convincing parasite mimic that is commonly seen in deep respiratory specimens: detached and intact cilia from respiratory epithelial host cells. The cilia on these structures will remain motile long after the cells are sloughed from the human host and thus resemble ciliated or flagellate parasites such as Balantidium coli and Trichomonas tenax. However, the morphologic features allow for clear differentiation of these objects. Detached ciliary tufts (DCTs) are relatively small (5-15 micrometers in diameter), the cilia are present in a dense mat attached to a terminal plate, and the cilia beat in a rhythmic motion without propelling the object forward.
In comparison, Arthur Morris notes that "B. coli is very (very!) large in its ciliated trophozoite form" (40-200 micrometers) "and is covered in short cilia rather than a localized patch of long cilia" (as seen in this case). "It also has a distinct peristome and kidney-shaped macronucleus which is not present here." The cilia on B. coli cause it to move in a 'rotary' or 'boring' motion.
Similarly, Trichomonas tenax is easily differentiated from DCTs by morphology. It has only 4 apical flagellae (rather than a tuft of dense cilia) and demonstrates a 'jerky' motility pattern.
Of note, the free-living amebae that infect humans (e.g. Naegleria fowleri) do not have a flagellate form in the human body and therefore should not enter the differential diagnosis when DCTs are seen. Also, Lophomonas blattarum is a parasite of cockroaches and has not been convincingly described from humans; instead, it has been misdiagnosed in cases where DCTs were observed.
HERE is another case from my blog, showing Papanicolaou-stained DCTs.
Also, HERE is an article (in Chinese) that discusses how previously-reported cases of L. blattarum infection were actually cases of misidentified bronchial ciliated epithelial cells.