Much has been said, mostly praising the very trivial exposure-of-true-Hollywood-glamour-emptiness aspect of this great movie. However, the movie deals with some interesting personal psychology as well - or perhaps - primarily.
The irony of the Holden character narrowly escaping his harsh creditors only to be much further (morally) indebted in his relationship with Swanson is most funny. He engages in a relationship without true commitment. As the story goes on, he even wants to replace the love he has created with Swanson for the love of a younger woman. The classic fall of the noir male character is elegantly underway.
The Swanson character is not evil. The murder she commits is not committed in cold blood, but as a result of the betrayal and lies of people she thought she could trust. I.e. Holden and the too kind director who does not have the courage to tell her the truth about herself.
When Holden's true intents towards Swanson are revealed the punishment is immediate, but of course, on her part, well over the limit. The development of his character in the movie is, however, more interesting.
I find the "kill-and-be-famous" ending of the movie to be a bit unnecessary even for the cynical story. It is true that a murder would probably be the only way for Wilder to convincingly dust off an old star and lead her back in to the fame light. Thus, however, Wilder chooses to prefer the theme about what leads to personal fame to the theme about betrayal of an indebted man and its consequences. The two themes do hardly float together like blood and water, even in a film noir, at least not in this one. It is great, though.