The trivia text box on the DVD says that the music in the "patriotic" frame story is an 1861 song, Battle Hymn of the Republic, by Julia Ward Howe. In fact, it is an 1856 tune called Say Brothers Will You Meet Us by William Steffe, which has been used as an accompanying tune by various poets. While Howe's song is unquestionably the most famous verse ever written for this tune, nothing Howe wrote is ever heard in this show.
The Robot has backward feet, yet in some long shots Micky Dolenz' normal feet can be seen. An example is when he leads Davy Jones and Peter Tork across the sand to the spaceship.
When Davy and Peter are discussing what to do with the duplicate Micky, Peter Tork mouths along to Davy Jones's dialogue.