I'm unable to tell which misconception would be among the top ten, but I can start with examples I heard.
First of all - there is one misconception that is also widespread among the users of phylogenetic nomenclature (though none of them is probably working on the
PhyloCode). It's the belief/opinion/conviction that clades are defined, which is untrue. This statement has been advocated by Stuessy (2000, 2001) who wrote that “individuals can be described or if you like defined (my preference would be ‘characterized’), but
not their names” (Stuessy, 2001: 185). As de Queiroz & Cantino (2001) replied to this, “individuals can be described or characterized, but
not defined; only their names can be defined” (p. 821), because “definitions apply only to words, not to the things to which the words correspond” (Ghiselin, 1966: 127).
Species are also clades.I heard that only once but I think that it is important to mention it. Of course, Species
are not clades in the sense they are always monophyletic. They are different kind of biological entity which form clades (monophyletic groups), but we
cannot require their monophyly.
The PhyloCode must introduce a lot of new names to name all clades.That's what I heard several times. It's, of course, nonsense! It's totally impossible to name all clades (and it would be even if we had perfectly recovered tree of life).
The PhyloCode needs perfectly preserved remains.Also untrue. It doesn't need it. People think that, because they are convinced that the
PhyloCode is unable to work with more than one phylogenetic hypothesis, which is incorrect. As I already wrote to Mike, I had a presentation about the
PhyloCode and phylogenetic nomenclature at Charles University. It was great experience for me but arguments were based mostly on misconceptions and misunderstandings. In one of my slides I had this picture:

It was used as an analogy to phylogenetic nomenclature (taxon name ~ the t-shirt, phylogenetic definition ~ the text, and taxon ~ beautiful girl who wears the T-Shirt). Taxon names are just like this T-Shirt. The only woman who will wear the T-Shirt is the one who loves Dan (assuming that there is only one Dan in the world). And what happens when there isn't such a girl? It's simple, no-one will wear it. So, the
PhyloCode doesn't need perfectly preserved remains because it knows how to work with weak phylogenetic hypotheses (it permits
qualifying clauses).
However, the most sad thing isn't the fact that they were convinced about it. It's the fact that I SAID that SEVERAL TIMES during my presentation but they didn't hear me (although they invited me).
ICZN and ICBN use phylogenetic definitions.It's funny but I heard this as an argument against the
PhyloCode: “why do you want the
PhyloCode while the rank-based codes also use phylogenetic definitions?” Rank-based codes DON'T use phylogenetic definitions. Well, we can define taxon names without the
PhyloCode, but people would use whatever they want, which is AGIANST the approach of phylogenetic nomenclature because one of the main points is universality (all scientists should use the same names for the same taxa).
Referencesde Queiroz, K. & Cantino, P. D. 2001. Taxon names, not taxa, are defined. Taxon 50: 821–826.
Ghiselin, M. T. 1966. An application of the theory of definitions to systematic principles. Systematic Zoology 15: 207-215.
Stuessy, T. F. 2000. Taxon names are not defined. Taxon 49: 231–233.
Stuessy, T. F. 2001. Taxon names are
still not defined. Taxon 50: 185–186.