Another possibility is Ed Wood's JAIL BAIT (1954). According the IMDB, the following goof is made: "Continuity: After the operation to change Vic Brady's face, the first time the bandages come off, the scar on his forehead runs diagonal from the top of his nose to well above the eye. However when he's shot by the pool, the scar runs laterally across the middle of his forehead."
Yessssssssssssss, that's the one, Jase! Well done! Strangely enough, I've just come from the "It Came From The Vault" forum and a fellow called Dumspter Diver came up with the same movie as you did. What a coincidence, two great minds thinking alike!
Now, your mention of Vic Brady standing by the pool is significant, because yes, it was at that part that the scar moved between frames, haha! I remember that now, and I had had vague recollections of a swimming pool.
Here's a link to a page that gives quite a bit of info on the movie:-http://www.mininova.org/tor/1233644
There's another part in that write-up that also jogged my memory, where the plastic surgeon's son's day-old murdered body suddenly falls in front of his father from behind a curtain - and his father hardly looks surprised at all!
Well, everyone, if you want to see an entertaining movie for its weirdness and inconsistencies, then this is the one to watch!
Thanks again Jase, matey, from the Ostrich bloke! Best wishes.