Hello!
I can only remember about the Holocaust as you said, so i'll give LOTS of information about it if that's fine with you :)
Here we go ...
Some will claim that the Holocaust paved the way for the birth of the State of Israel. This is partially true, but it was primarily the courage of the Jews themselves that did the trick. Some will claim that it made the world aware of Genocide. This is only partially true as the genocide of the Armenians preceded it. In a very real sense, its primary effect was in hindering Hitler's war effort thus making his defeat more of a sure thing.
1. The Holocaust can be considered to have begun in 1933 with Hitler's coming to power in Germany, and proceeded from that time in stages. The first stage was the Nuremberg Laws, the first of which was passed in 1933. They began and continued a policy or making the Jews second class citizens, denying them employment in various fields--such as teachers, lawyers, etc.--denying them equal rights with "Aryans," and leading eventually to taking away their citizenship altogether. Many of Germanys Jews were thus compelled to flee Germany, and many of these were Nobel Prize winners, university professors, and scientists--Freud, Einstein, etc..--who would end up in the US and Great Britain. As you will recall, Einstein was the one who first alerted FDR to the possibility of nuclear weapons, and it was expatriated German Jews who were instrumental in making the Manhattan Project a success. These same Jews--and many, many more in various fields of research and weapons development--helped Hitler's enemies win the war. Had Hitler not driven away all these talented scientists, they'd have been on Germanys side, as they were in WW1--the fellows who invented Germanys poison gas weapons, advanced drugs to treat the war wounded, etc., were Jews--and would have been developing weapons for Hitler, not FDR.
2. Once the war started, and the Final Solution was implemented, every guard who now had to deal with killing Jews was not available for duty on the Front. Every able-bodied Jew--Jews who would have fought for Germany as they had during WW1--who was killed in the gas chambers was not available for duty on the Front. All the materials utilized to build concentration camps and gas chambers were not available to build defenses such as tank traps on the Front.
3. In the wars final stages, as the Red Army was approaching from the East and Patton and Bradley were approaching from the West, Hitler gave first priority to transporting Jews to Death Camps instead of soldiers to the Front, his hatred of them was that great.
4. Another unintended effect of the Holocaust occurred after the first Death Camps were liberated by the Allies. When the Allied soldiers, many of whom were themselves Jewish, saw what the Germans had been doing, they tended to stop taking German prisoners, especially members of the Waffen-SS, and executed them instead.
5. The Nazis did utilize slave labor, but the type of slave labor they utilized Jews for was not really meant for production as such, but to further a policy of "Death Through Work." As such, it was very inefficient and tended to be very counterproductive. 6. Those Jews who managed to escape the walled-off ghettos or Death Camps formed partisan bands behind the lines that engaged in sabotage and other efforts to stymie the Nazi war machine. Many divisions of German soldiers had to be engaged behind the lines to fight these partisans rather than take Stalingrad or protect Omaha Beach.
All things considered, the Holocaust had an entirely negative effect on the Nazi war effort.
Hope this Helps! Have A Wonderful Day! :)