According to Reid J. Epstein, "Republican debate: 7 attacks on Newt Gingrich to watch", 1210/2011:
“Gov. Romney is much more disciplined in his approach and much more thoughtful about what he says and how he says them,” Iowa state Rep. Renee Schulte said in a Romney campaign press call Friday.
Ms. Schulte may very well have been misquoted or quoted without essential context, but it's not surprising for someone to use a plural pronoun that co-refers with the referent of a fused relative clause introduced by what. Although "what he says" is morphosyntactically singular, a paraphrase with an overt head is likely to be plural: "the things (that) he says", etc.
Some similar examples:
Much of this comedy is built into Tom's frequent and ignorant fulminations against the colored race, Western civilization, women, and even men's clothing. The comedy is expressed in his actions, no doubt, but it comes out more in what he says and how he says them. [Gautam Kundu, Fitzgerald and the influence of film, 2008]
I began having the opportunity to share Tanya's testimony with others. I shared how, as a child, Tanya never did much to please me. I always found things wrong with what she did and how she did them. [Barbara J. Woodall, Help! I don't like my child, 2008]
This above is a quick summary of how God created the heavens and the earth. God is very specific in detail about what He created and when He created them. [Dwight O. Troyer, Genesis 1-2-3, 2007]
It's true that there's a related construction with a plural noun following what: "… it comes out more in what things he says and how he says them", etc.
It's also true that pronouns can refer to things evoked but not overtly mentioned in the previous discourse.
So are these examples ungrammatical? Perhaps they're just "ill-written and discourteous".