story identification - Older science fiction book about time travel to retrieve things but they went sideways through the dimensions instead

So, as I vaguely remember it. It was set in the distant future were a dictator rules the Earth. By this point carbon dioxide was so high most life outside of humans was extinct. So the dictator built a special zoo with the right atmospheric conditions. Then he sent crews back in time to retrieve things. But, unbeknownst to them they were sliding sideways through the dimensions. So when they went to get a horse they got a unicorn instead, a real drake instead of a komodo dragon, etc. The unicorn gored one of them really bad. The drake burned another pretty bad.

Somewhere along the way they speculate on what happened to the rocs of myth and figured it was the ostrich and they re-enabled the disabled DNA pairs and suddenly had a roc that broke free, escaped, and quickly suffocated to death in the high CO2 atmosphere.

I remember them all nearly dying because someone sent to get the first automobile built by Henry Ford screwed up and accidentally destroyed the original. And that changed time so that Ford never started an auto industry so the air never got polluted, etc., and everyone in the future, accustomed to the high CO2, was dying without it.

Does anyone know the author and book/story names?

Answer

This is The Flight of the Horse by Larry Niven. It's a fixup novel built from a compilation of stories about the hapless Hanville Svetz who is tasked with retrieving the things you mention.

The collection of the unicorn is the first story. During the mission Svetz collapses because his metabolism is adapted to the high carbon dioxide levels of modern Earth and when he goes to the parallel Earth with low CO2 he forgets to breathe:

The air of the cage was the air of Svetz's own time, and was nearly four percent carbon dioxide. The air of 750 Ante Atomic held barely a tenth of that. Man was a rare animal here and now. He had breathed little air, he had destroyed few forests, he had burnt scant fuel since the dawn of time.

But industrial civilization meant combustion. Combustion meant carbon dioxide thickening in the atmosphere many times faster than the green plants could turn it back to oxygen. Svetz was at the far end of two thousand years of adaptation to air rich in CO2.

It takes a concentration of carbon dioxide to trigger the autonomic nerves in the lymph glands in a man's left armpit. Svetz had fainted because he wasn't breathing.