After Bart throws the ball through the window glass, every later shot that has the window visible shows no hole or broken glass. Further, the sound of the glass breaking is too late after the ball is thrown.
When Elsa is speaking in Lylah's voice, if you look closely you can see that the words are slightly out of sync with Elsa's mouth.
During the opening credits, Elsa is supposedly walking along the Hollywood Walk of Fame and she looks at the stars for Roscoe 'Fatty' Arbuckle, Jean Harlow, Clark Gable, Marilyn Monroe, and Rudolph Valentino in less than one block. In reality these stars are stretched along Hollywood Boulevard for several blocks and Gable's is over on Vine Street. Also, Arbuckle's star has his name Roscoe on it and not his nickname of "Fatty".
Elsa's (Kim Novak's) voice during her tirade against Molly Luther is clearly not hers. It is the guttural deep voice of an older heavy smoker, something that cannot be imitated. This is consistent with the plot, which eventually reveals she really is possessed...but why doesn't anyone else notice the impossibility?