Max was introduced with the intention of spinning him off into his own series. However, the network decided not to buy the new show, and Max instead was used as a companion for Jamie throughout the rest of the series.
This was the first episode broadcast on the National Broadcasting Company.
Jaime's indignant commenting about how nice Max's cage was, but that it's still a cage, unwittingly foreshadows the final episode On the Run (1978) which speaks about the lovely resort that the government would want to place Jaime in, but where she could never be truly happy because she would be confined to a specific area, not free to ramble and roam the big outside world as she pleased.
Maxamillion is possibly named this for at least two reasons; the cost of the making of the fictitious dog, as explained in this episode or that, he my have, too, been named after the founder of this breed Max Emil Friedrich von Stephanitz (December 30th, 1864 - 22nd April 1936); the first German Shepard dog was named Horand von Grafrath (b. January 1st, 1895) and the genetic basis for modern German Shepherds seen today.