I've always enjoyed Brian's shows and lectures. But this is such a big load of crap.
First, the things he does explain he doesn't do very well. Why are orbitals like a spring vibrating? What's happening when hydrogen burns? Etc.
But, at the end, I almost started gagging. He was trying to imply that Pauli's exclusion principle demands that every electron in the universe is connected to every other electron in the universe. i.e. When you heat a cup of tea, every electron in the universe adjusts it quantum state slightly to ensure that no two will be identical.
A great big "boo" on you, Brian Cox.