To those who complain about the dialogue...
Many modern (and younger--that is, under-thirty) viewers often complain about the dialogue in Double Indemnity, calling it "cheesy" or "unnatural." To make this criticism, however, is to ignore context and thus to miss the point.
Most dialogue in movies--particularly in movies made during the Hollywood Golden Age--is heightened and stylized. It's a convention. When we go to the movies, we usually expect the characters to talk in a way that distills the essence of human conversation. If movie talk exactly duplicated the way people talk, movies wouldn't be an art form. It's that simple.
Well, it's almost that simple. I know that the "hardboiled" narration and dialogue in Double Indemnity may strike modern viewers as REALLY sytlized--perphaps to a fault. But, of course, this hardboiled stylization (which includes the many, many times Neff calls Phyllis "Baby") is another convention--a convention of the pulp crime/detective fiction made popular by such writers as James M. Cain and Raymond Chandler, both of whose names are listed in the credits of Double Indemnity.
Movie conventions are defined as an agreement between filmmaker and viewer that certain rules--even patently phony ones, by certain standards of realism--will be accepted. (That's why, to invoke another genre, viewers accept Julie Andrews bursting into song on a mountaintop.)
The over-the-top tough talk and fancy, self-conscious figurative language in Double Indemnity are just part of the genre. Those who accept this fact will surely find the film even more enjoyable.