The Bad Seed was also one of a number of mid-'50s movies that took most of their casts from Broadway; in this case Nancy Kelly (as the mother), Patty McCormick (as the evil kid) and several other actors were repeating the roles they'd played in the Broadway play. And apart from the infamous tacked-on Hollywood ending, the script is pretty faithful to the play. It's one of a number of very "stagey" movies Warner Brothers made in this era; others were the adaptations of the musicals The Pajama Game and Damn Yankees (both with nearly the entire casts of the Broadway shows) and No Time For Sergeants (with Andy Griffith repeating his stage role). Essentially, Warner Brothers was responding to the collapse of the studio system -- the fact that they no longer had enough "in-house" stars to staff a picture -- by making extensive use of Broadway talent to fill their pictures. It worked, too, though all these films now look a little drab and stagey.
Patty McCormick has done a commentary track for the new Bad Seed DVD; here's what she had to say about the film in an article a few years ago:
The Bad Seed has become a camp classic. But for me, personally, I spent a lot of years pretending it never existed. I was almost embarrassed by that film. Now for some reason, everybody is looking at it fondly as all those movies and TV shows of the '50s and '60s are being embraced. After so many years of trying to push it aside, I now feel I have grown to appreciate what I did back then. And I have to say, I like it.
Addendum: It seems my memory may have played tricks on me and caused me to overrate the influence of pop-Freudianism on The Bad Seed. See comments section. However, I choose to blame my bad memory on a suppressed Oedipal conflict.