What civil rights in The Long Good Bye would be outdated now?

The Los Angeles Police Department, as portrayed by Raymond Chandler in The Long Goodbye, has no conception of civil rights. For one thing, detectives in the story interrogate suspects without reading them their constitutional rights. It wouldn't be until much later, in the landmark Supreme Court case of Miranda v Arizona (1966) that police officers would be required to read criminal suspects their rights before questioning them. You've doubtless seen many cop shows and movies where this is standard procedure (e.g., "You have the right to remain silent . . .").
The LAPD is also portrayed as institutionally racist. All Hispanics are contemptuously referred to as "Mexican," whatever their cultural background. Marlowe himself is not immune to the prevailing racist attitudes. As he speeds over to the Wade residence, he imagines what could've prompted Mr. Wade's distressed phone call. One of the possible scenarios Marlowe envisages consists of Mrs. Wade's being chased by a "big buck Negro with a meat cleaver." This is an expression of a prejudice—widespread at the time—that African American males were sex predators who represented a danger to white women.