Cheryl Ladd (credited as Cherie Moor) provided the singing voice for Melody Valentine. (Really, a stage name for a cartoon?)
Patrice Holloway, sister of Motown singer Brenda Holloway, provided the singing voice of Valerie and sings lead on the theme song. Brenda Holloway is best known (at least by me) as writing, "You've Made Me So Very Happy" which was a moderate hit for her but a huge hit for Blood,.Sweat and Tears. Their success with the song led to her sue Berry Gordy (she won!).
Which leads us to our next bit of trivia which is not the least bit trivial, the series was the first original American Saturday-morning animated series to feature an African American character: the tambourine player Valerie. Hanna-Barbera wanted to change Valerie to a Caucasian even though she was already established as African-American in the Archie comics (I know this was still only the early 70s but really, how ridiculous and petty is that?). So they wanted to fire Patrice Holloway who had been cast as Valerie's singing voice. But Danny Janssen, who was producing the real-life group's Capitol album, refused to fire Holloway (good for him!) and Hanna-Barbera relented.
In the series' original opening sequence, Alexandra attempts to blow up the band... but, like Wile E. Coyote, is herself blown up. When edited for re-broadcast, this sequence, coming toward the end of the theme song, is replaced with more footage of Josie and the Pussycats dancing (This surprised me, I thought this editing out of violence didn't start until at least the 90s) but, because the sound of the explosion is part of the theme track, the explosion itself has been left intact (even more reason to just leave the original sequence alone!)