Well, of course you can use both tenses in a sentence because they can refer to different acctions. Consider:
I agree [NOW] that he was wrong [THEN, two days or weeks ago, whenever in the past].
I don’t care [NOW] if she had a character development towards the end [end of what? her life? her career? her university? Could be any past period of her life that is now finished].
But unless you specify the complaints of the person who stated that these sentences are not correct, I can't think of anything else to say.