Sexism

Perhaps they realized that hyphenated names are a bad idea, especially after a few generations of the practice. Hardly sexism in any case.

Racism

IIRC Star Trek was the first show to have an interracial kiss, so critisisms on that front fall kind of flat. Besides, did any other TV show in the 60's have that much diversity?

Pet Overpopulation

3 unneutered tomcats on a ship with over 1000 people, (I think, feel free to correct me.) and a few puppies being born. Where do you think they come from, the replicators?