The first thing to note is that while Neil has a great science education he apparently knows little or nothing about theology, specifically Christian theology.
From the Christian perspective God did create a perfect universe but then when Adam and Eve sinned they shattered the perfection of the universe. In Eden the lion didn't eat the lamb, no one got sick, etc but when man sinned that changed. Hence even if one could find "bad design" in the universe it wouldn't say anything about God.
But even ignoring that Neil said a lot of things that are logically wrong.
The first point he made, as I recall, was that the universe was too big. Why make such a huge place just for people on Earth?
The first, and most obvious, objection is that Neil is an astrophysicist. He so loves studying this vast universe that, when not attacking Christianity, he dedicates his life to researching it. Given that creating the universe is trivial for God it would seem obvious that God may have created this huge universe simply to provide amusement for people like Neil; sort of like the mobiles parents put over their babies cribs.
The next objection is that Neil has no idea how many worlds full of people with souls there are in the universe so he really can't say that the "huge" universe is wasted.
Neil also mentioned that supernova's were a sign of bad design because when they blow up they kill life over a huge region of space. That sounds bad except that if the only place in the universe that matters is Earth--critical for Neil's argument that the universe is too big--unless a supernova wipes out life on Earth supernova's explosive tendencies are only good not bad.
Why good? Well it turns out that all of the heavy elements, pretty much everything beyond oxygen, in the universe are created in supernova's. Without supernova's there'd be nothing to make a world like Earth out of; no iron, no lead etc.
According to Neil then the fact that there are supernova's that make life possible is a sign of bad design. Right.
Neil made a bunch of other equally illogical and baseless points which I don't happen to recall, and I'm not wasting another 5 minutes of my life on his "reasoning", all of which are based on a singularly large case of conceit on Neil's part; that if something doesn't make sense to Neil then it can't be right.
Essentially what Neil is saying is that he is smarter and better informed that an all knowing all powerful God. If Neil didn't claim that then he couldn't say that what he considers poor design is evidence against God. After all if we could prove that God exists and we still see those examples of "poor" design it would simply mean we don't understand things as well as God does.
Similarly if we see something Neil considers "poor" design it could mean there is no designer, no God, or that we just don't appreciate how wonderful that "poor" design really is.
Neil is a great example of how scientists who don't understand philosophy, religion, or the basic tenants of science--if you can't experiment on it theories are mostly guesses-- are more than glad to politicize "science" to serve modern liberalism.