The choice of prepositions for this kind of expression is really arbitrary and sometimes varies by region. Most people are used to the expression "wrong with" meaning a defect, whereas wrong meaning incorrect might take "in." For example, the use of the Cyrillic alphabet would be wrong in this context.
Solecism (in the sense “Error in the use of language”), a rather general term that encompasses grammar mistakes, is one possibility. Another general term is infelicity. A few dozen quite-specific kinds of language errors (mostly stylistic rather than grammatical) are explained in BYU's Stylistic Vices webpage, for example pleonasm, “Use of more words than is necessary semantically. Rhetorical repetition that is grammatically superfluous” or acyrologia, “An incorrect use of words, especially the use of words that sound alike but are far in meaning from the speaker's intentions” (like malapropism, eggcorns, etc) and many more.
For verbs, consider misspeak (“To fail to pronounce, utter, or speak correctly”). A wikipedia article called Misspeaking says
Misspeaking is a word used to describe the act of speaking “incorrectly, unclearly, or misleadingly”, to “fail to convey the meaning one intends by one’s words”
Also consider the form to err grammatically. Verb err means to make a mistake; to err grammatically is to make a mistake in grammar.
Best Answer
The second sentence is correct.
'Error' is a noun. It describes something that is wrong.
'Wrong' is an adjective, and so is applied to the subject ('this sentence') to describe it.
To write a correct sentence with the same meaning as the second one, while using 'error', you would say something like: