I remember this short story as very funny. It was told in retrospect in the first person by a member of a fairly slap-happy team of inventors developing a new teleportation device.
Initially, there are some amusing experiments with rabbits, I think. And I distinctly remember that they were sued by an irate female film star or celeb because she arrived with her nose in the wrong place. There were also further disasters and law suits.
I think I read this c.1978-79 in a cheap anthology.