My first question is what things plout? The Word Sketch produced by the CZES corpus tells us:
vessels on water: loď, trajekt, parník, člun
creature on water: labuť
in the sky: balon, mrak, měsíc
vessel in water: ponorka
creature in water: ryba
The first three categories may well float and sail - I don't have time to look them up in an English corpus at the moment, but native speaker intuition tells me this is the case. But things in water do not float or sail, so plout has different fields of reference - an obvious error trap. Vessels on water more typically come and go in English. And creatures on water typically glide.
A formal matter concerns its conjugation and aspect.
As a verb of motion, I would not expect to form its future with budu, and there are only seven examples in CZES. And I can't remember now how the future is formed. More study required.
The significant prepositions that follow it can be seen in this extract from the Word Sketch. Because plout is a verb of motion, the prepositions which can take more than one case (na, pod, nad, mezi) could be expected to take accusative. But this is not the case (no pun intended). The prepositions expressing where plout takes place, quite logically, take locative. For example, plout na:
Pes s námi pluje na člunu (interesting 3rd pers sing, not 1st pers pl.)
Vladimir Putin pluje na vlně popularity (metaphorical use of wave)
Mostecký kostel pluje na vodězbytek rostliny plul na hladině.
Nakonec všichni plujeme na jedné lodi.
Balon plul na západ (rare example of accusative.)
Even though there is no case alternation with po, it's significance is worth noting. Some examples:
Měsíc pluje po hladině rybníka.
Bez pití a jídla pluli po Indickém oceánu čtyři indonéští rybáři
Adéla Stodolová se svým bříškem pyšně pluje po jevišti,
Docela v předu pluje po jezeře loďka.
Plout po moři je snem mnoha Čechů,
a měsíc, jak skvostně pluje po obloze.
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