Usage question "any" - paging copyeditors

[jack]

Can I say "My book doesn't have any major mistake?"[1] I'm suddenly unsure, and google doesn't help because 'any' is too common a word. Andor does anyone have OED?

[1] Originally 'faux pas', but that's confusing because it's spelt the same in singular and plural.

Comments

[chess]

My brain dislikes it, and would probably insert an 's' after 'mistake' if it was in a bit of text I was proofreading.