Who the Hell Killed Owen Taylor?

As I've read The Big Sleep I didn't have any issues with some of the massive plot holes in the movie. There is no satisfying reason in the film for why Carol Lundgren would want to shoot Joe Brody. The homosexuality between the characters is present in the screen play but was removed from the final film because of the Hays Code.
The Big Sleep may be a classic display of Bogie and Bacall. It may be a classic piece of film noir. It's also a classic example of post war fear of corruption coming from the arts.
The Big Sleep is dealing with the underbelly of Hollywood. There's pornography, gambling, sexuality, and plenty of drinking. What we get in the film is an innuendo filled story that lacks the punch because the plot is censored.
Where as in the book Reagan was Vivian's husband, the film just has him as an employee of Sternwood. This is because you can't have Vivian in a relationship with Reagan and in anyway involved in his death. Mars killed Regan. Really? During that last scene I was unconvinced. I was more convinced when Vivian tried to say she killed him, and even then I didn't believe it. Mars has no real motive to commit the murder. He also has enough connections to not need Mars being believed to be in Mexico. HE also wouldn't need to hide his wife away.
I felt bad for the actress that played Carmen. She was practically cut out of the film because her performance out-shined Bacall's. Her character was central to the plot but she got no real chance to show how much of a danger she could be.
Do they ever really explain Geiger's business? I mean you know that Brody took it over but there's never a good idea of what it really is. Other than not "first editions".
The movie suffered greatly from a restrictive code. The screenplay did a good job of getting the grittiness of the novel.
Well I'd rather get wet in here than out there.