What's wrong with 'caught no mice'?

It's the verb tense.

*I'm not going to keep cats who caught no mice.

is wrong, it should be "catch no mice" or "who have caught no mice."

There is nothing wrong with the grammar of the quoted section (caught no mice); either the speaker was being overly finicky and misjudged the grammar, or he is referring to the grammaticality of the rest of the "large and vague threats".

The sentence sounds correct only because the narrator is speaking in the past tense, so "he wasn't going to keep a cat who caught no mice" sounds correct.

Since "caught no mice" is quoted, it can be assumed it's extradite from another, slightly different quote. I'd assume the character who originally spoke the sentencebeing later references would have been speaking in the present tense, as in "I'm not going to keep any cats who..." in which case "caught no mice." would be incorrect grammar. It would have to be "catch no mice" or "haven't caught any mice."

(Please excuse the poor formatting, sent from my iPhone.)

The error must be in the three words in inverted commas "caught no mice." I think it is in the plural "mice". It should be "mouse": if one mouse is singular, no mouse is even less plural, a fortiore.