Double Indemnity is most definitely a classic film. Lots of interesting tidbits about it. For example, as Susan cited, there is that great subtext "motorcycle" dialogue, but if you look closely, after Phyllis visits Neff in his apartment, basically throwing herself at him, when she leaves, he shuts the door, turns back into his living room. Notices the corner of his rug is flipped up. He gives it a little kick with his shoe. I'm sure this bit of business is to infer that he and Phyllis did some rolling around on the ground in their unseen sex scene. Filmmakers had to use dialogue and visual subtext to get around the Hayes Code, lots of it in DI.
The bromance between Walter and Keyes is another interesting dynamic, a lot of subtext in their conversations. I particularly like the bit of business where Walter lights a match for Keyes several times by flicking his thumb across the match head... which at the very end of the movie Keyes reciprocates for Walter when the latter can't find the strength - due to his wounds - to do it himself. A nice callback.
Then there's the famous gas chamber scene with Billy Wilder shot, but ended up scrapping. There is one photograph of that set -- the film was destroyed -- and here is the
photo. And
here where Wilder talks about the alternate ending which he cut.
And oh yeah,
here is a photograph of the one scene in which Raymond Chandler appears. Chandler and Wilder did not get along at all, but evidently their conflict benefited the script, helping to make DI the classic it is.