Deliberate mistake: When the Darlings discover the dead rat, they raise the curtain and cry out loud, but the rat is nowhere to be seen. Given Disney's long time history of refusals to show dead bodies or blood, it's highly possible that this was a deliberate mistake, but really awkward indeed.
Deliberate mistake: Glenn Ford strikes the window in the library door with his briefcase and it instantly shatters. In reality, a blow delivered by a briefcase to a plate glass window would have produced no more than a scratch or crack.