First, “say something wrong” often has the sense of being insensitive or hurtful. It wouldn’t be a natural choice if you’re talking about language errors.
As far as the tense, both are ok but “say” would would be better if the request is habitual. Also to be considered is “I’ve said”. “Saying” is slightly incompatible with “the second” because but certainly something you could hear.
I’m making mistakes, aren’t I? Tell me when I do.
Tell me the second I make a mistake. (In general)
Tell me the second I’ve made a mistake. (The first one)