I am trying to remember the title of a story where a man is sent back in time to collect extinct animals for his era's zoo. For some reason, he only locates and brings back mythical creatures. I read it in the 1980's.
This sounds like "The Flight of the Horse", by Larry Niven. Published 1969, it was the first of a few short stories starring Hanville Svetz, agent from a badly confused future sent back to retrieve (usually misidentified) animals from the past.
There were about five stories in this series, reprinted as a collection in 1975.
They were republished, with a new novella added, as Rainbow Mars in 1999.