Your example is a “past real conditional”. The speaker doesn’t know whether or not the man said it, but it is considered possible. If it is true, then the speaker believes that the man made a big mistake. Contrast that with a present unreal conditional: “If he said that, it would be a big mistake”. He is not presently saying that. The past unreal (contrary to fact) conditional: “If he had said that (but he didn’t), it would have been a big mistake (but it wasn’t, since he didn't say that).

Phil explains: yes. You can say it. He also gives the differences in meaning between similar sentences.