I heard the story mainly as a period piece. A period piece from a great writer in a good period, to be sure, but definitely something from another era -- much like reading Wells or Verne today. Fun, but a different kind of fun than reading a story written in the current period, and requiring a different set of expectations.
I found the "expectation adjustment" was necessary not only for the technical details -- our understanding of dinosaurs has changed a lot since the story was written -- but also from the standpoint of the story itself. The narrative device of, "here, let me tell you this long anecdote to justify a decision or illustrate a point" is much less common today than it was in the heyday of Clarke and Asimov, when whole story collections were built around it.
Also, the long, expository info-dump laying out the "rules" for time travel would probably earn you a bounce from most editors today. Style changes generally require today's authors to work their world-building in via character reactions and unfolding action, rather than narrating "here, this is how this works." Consider the difference between how de Camp handles his exposition on time travel in this story and the way Ferrett Steinmetz handles his explanation of how ad faeries affected the world in Dead Merchandise.
Still, good fun, and I think the narrator did a bang-up job. I'm glad matweller was able to fix restarts in the narration. They took me out of the story as I was listening, so that was definitely worth fixing. Thanks!