Correspondents have pointed out some further examples of Pseudo-Latin Plurals. The cases that I have previously mentioned involve incorrect choices of stem form and ending. The new examples involve attempts to make plurals of things that in Latin were not nouns.
Donald Davidson brings to our attention sub poenae, intended as the plural of sub poena. In legal English sub poena is used as a noun to refer to a court order for a witness to appear or to produce documents or other evidence. In the later usage it is short for sub poena duces tecum "Under penalty you will bring with you". duces is the verb "you will bring". tecum is the combination of the pronoun te "you (singular)" and the preposition cum "with". sub poena is a prepositional phrase consisting of the preposition sub "under" and the noun poena "penalty". A prepositional phrase is not a noun and cannot be made plural by changing the ending of its noun to the plural. Indeed, the nominal part of this prepositional phrase is not in the nominative case. sub governs the ablative case. The way Latin is normally written, you can't tell, but the /a/ of sub poena is long whereas the /a/ of the nominative singular poena is short. You could of course put poena into the ablative plural, but sub poenis (with long /i/) would mean "under penalties". In short, sub poena is a noun only in English, not in Latin, so the only way to make it plural is the English way: sub poenas.
Claire Bowern of Anggarrgoon has encountered non sequituri, intended as the plural of non sequitur. In Latin, non sequitur is a sentence, not a noun. It consists of non "not" and the verb sequitur "it follows". As a sentence, it cannot be made plural by adding the nominative plural suffix for second declension nouns. As an English noun, it has the English plural non sequiturs. If we really wanted to make a Latin plural, we could, since in this case the verb could be made plural - non sequiuntur would mean "they do not follow". That might be a little obscure.
[Update: Keith Ivey has pointed out another example of this type, ignoramus, which is sometimes given the plural ignorami, e.g. here. This would be correct if ignoramus were a second declension noun, but it isn't. ignoramus is a verb meaning "we are ignorant of". It became a noun through its use as the name of a character in the 1615 play by George Ruggle of the same name.]
[Update: John Kozak mentions seeing agendae which I too have encountered from time to time. Google turned up plenty of examples, perhaps the most embarassing of which is this list of information about meetings at the University of North Texas . The problem here is that agenda is the plural of agendum "something to be done"; there is no singular agenda for agendae to be the plural of. Of course, in English agenda is used as a singular noun, so there is no reason we shouldn't use the English plural agendas.]
[Update: Keith Ivey has pointed out a similar example: omnibus, which is sometimes given the plural omnibi, as here. omnibus is a noun, or, to be precise, an adjective used as a noun, but it is already plural and in the dative case. omnibus is the dative plural of omnis "all" and means "for all". It therefore cannot be further inflected as if it were a nominative singular noun. ]