To clarify - The Allies obviously recognized the way things were run or done within Nazi Germany and wanted to change that did the horrors they unleashed were never brought forth again. However, when it came to formulating the 4 Allied zones and eventually the two German states, were there any laws, administrative functions, political boundaries, etc., that were kept because they were deemed to have worked or at the very least, make things run more efficiently until better solutions were found?
I'll copy-edit an older answer about women and Murder, which relates to a very specific part of your question: Laws. More specifically, the distinction of Murder and Manslaughter (Mord and Totschlag in German). (The women-related parts have been edited out of this answer.)
Some quick terminology from german criminal law: when the Nazis reformed the criminal law concerning "attempts on a person's life" , they differentiated the voluntary and purposely killing of a Person into 2 seperate crimes: Murder, punishable by death, no exceptions, and manslaughter, punishable by prison time up to "life without Parole" , but very variable.
Nazi criminal legal ideology was based on what german legal scholars call the "Typenlehre", or "type theory" (not sure about english translations, so pleas excuse my missuse of english legal Terms Overall). According to this theory, people didn't commit crimes, they were by their nature and type criminals, rotten to the core of their very personality. It was a very subjective, perpetrator-, instead of act-focussed idea. Now, the "murderer" was painted as the heinous, outrageous, untermensch , compared to the honorable, aryan "manslaughterer". I'll leave out perversion, Greed, etc , and focus on "Heimtücke" , perfidiousness. By perfidiously (from behind, in their sleep, with poison), instead of honorably (in combat, with a warning, giving a fighting Chance), killing their victim, the murderer revealed themselves to be not of true honorable aryan blood, and thus a despicable untermensch, sentenced to death. A honorable Germanic Killer, on the other hand, can take their gun, their smash hammer, or whatever weapon/tool is available, and take it out on their victim "fair and honorably", in best case avoiding prison time alltogether, if the judge is "understanding."
Throughout the history of modern germany, the FRG has struggled with her Nazi legacy in the criminal law, and many attempts to Reform §211 (Murder) and § 212 (manslaughter) have been made - the death penalty was abolished, and changed to life in prison (later, amended to always include the possibility of parole by our constitutional court), but the underlying Problematic base structure of the "Typenlehre" persists (Falling short before the 20 year rule i'll end here) up to the late 90s.
Entertaining side note: the current german in effect regulation on the Maximum height of Jägerzäune, a specific type of small garden fence, is also "Nazi legislation", as it was during the Third Reich that the necessary increase to just about 1 Meter Maximum was enacted.