The assumption of both above comments is that there can be multiple commonly-used definitions of a word. Annoyance is using one of the commonly-used definitions that doesn’t fit into the ‘most’ above. He asserts that the other definitions are not only incorrect but insane, and I think this answers your question—a definition can be incorrect in the case that it is insane. Though I think calling a definition ‘insane’ is an odd use of the word.
How can a definition be incorrect?
If you find the common usage incoherent or otherwise not useful, don’t use it. To do otherwise is to lie.
The assumption of both above comments is that there can be multiple commonly-used definitions of a word. Annoyance is using one of the commonly-used definitions that doesn’t fit into the ‘most’ above. He asserts that the other definitions are not only incorrect but insane, and I think this answers your question—a definition can be incorrect in the case that it is insane. Though I think calling a definition ‘insane’ is an odd use of the word.