[[WMG: Mary Richards is actually [[TheDickVanDykeShow Laura Petrie]],]]
who changed her name, after divorcing Rob, taking her son's first name "Richie" as her new fake last name. She did this because she wanted to start a career in the entertainment industry but her ex-husband was a famous television writer, and she was concerned that gossip about their messy divorce might hurt her career if people made the connection between them.
* Maybe this is obvious and you're basing you're theory off it but that's supposedly why the network made Mary single instead of divorced. They were concerned that viewers would think that she divorced Rob Petrie.
[[WMG: Murray was meant to be gay]]
Murray seems mildly effeminate and throws out a lot of catty remarks. This would be a toned down version of gay stereotypes of the era. The writers thought of him as gay and Gavin MacLeod played him that way, but couldn't actually make him gay due to standards of the time. This is how he wound up having a wife and kids, as well as a couple of plots where Murray is tempted by other women- for plausible deniability.