When Wilbur is explaining to the vet Dr. Baker about Mister Ed having amnesia, Wilbur makes a passing reference about his horse telling him not to remember anything, which Dr. Baker does not react in any way considering that, aside from Wilbur, no one knows about Mister Ed's ability to talk.
If Ed has amnesia, and thinks he's a person, why doesn't he remember he only talks to Wilbur and instead speak to everyone.