The Nazis sterilized well over 300,000 people; as /u/ramak__ noted, the decision as to who would be sterilized was not scientific but political. As an example, many people were sterilized for alcoholism but the vast majority were from a lower-class background.
The sterilization program was just the beginning. Many Nazi radicals wanted to expand the program to the killing of adults and children deemed disabled, but Hitler refused to start this program until war came - he knew very well that the public would balk. In fact, public dissent forced the government to suspend their "euthanasia" program in 1941 but not before the development of gassing and other techniques which would be applied to German mass-murder programs in the East.
Did it "work"?
No.
Nazi Germany killed or sterilized at least three-quarters of all diagnosed schizophrenics. Within a few years after the war's end, however, the rates began to rise again. Today, schizophrenia rates in Germany are actually higher than in the United States or many other European countries. Source, including info on the Nazi actions against schizophrenics.
Comparisons about Down syndrome are tricky for a number of reasons; the United States was a pioneer in sterilizing Down syndrome patients, for example, and abortion and fetal testing have made country-by-country comparisons over the last couple of generations tougher. However, as you can see here, the incidence rate in Germany are not far from the rate in other European countries.
There are similar results for many other categories of disease, even the hereditary ones; of course, this doesn't account for the influx of ethnic German refugees after the war, or postwar immigration from Turkey and other nations, or the widespread rape that followed occupation in 1945. None of these caveats should outweigh the central points about Germany's sterilization program; it perverted scientific language to meet political goals. It was criminally sloppy about identifying the "problems" it meant to solve and the solution applied was inhuman, ineffective, and unscientific. It was not worth the cost. It never would have been.
It's important to remember that Action T4 etc weren't very scientific. As well as euthanasing people, the Nazis also sterilized people. They sterilized people who were black (Afro-Germans). They sterilized people who were criminals or prostitutes, hardly examples of "bad genes".
It was inconsistent. Someone who was physically disabled was viewed as "a drain on the state" and was to be euthanised. An opponent at the time, pointing out the absurdity, wondered if that would apply to soldiers who were wounded in war
And of course they "euthanised" many Jews, Communists, Roma and gays.
Source: R J Evans Third Reich in Power & Third Reich at War.