I've been reading "The Rise and Fall of the Third Reich" and, among other surprises, it portrays Nazi Germany as a kind of anti-science country, teaching "German Physics," "German Chemistry," and so on, which rejected major scientific development and theories such as general relativity. "The Making of the Atomic Bomb" seems to confirm what "The Rise and Fall of the Third Reich" portrays: many of the greatest scientists of the time (Einstein, Planck IIRC) fled Nazi Germany. Though it seems like before the Nazification of Germany, Berlin was a scientific center of the world, the expulsion and censorship of science seemed to be a big deal under the Third Reich.
Opposite this is that in popular media (games, TV shows, works of fiction), the Nazis are often portrayed as geniuses with scientific achievements far beyond the other countries and powers of its time. To corroborate this, there did seem to be novel advances in Germany especially related to Werner Von Braun and rocketry. The question remains whether these successes were just piggybacking on the successes made during in the Weimar Republic or were actually correlated to Nazi policies and ingenuity.
Was Nazi Germany leading the world in science during the Third Reich, or is this an inaccurate portrayal of history?
The Deutsche Physik (anti-Jewish physics) movement was much more limited than many popular and older works portray it has having been. You should see it less as "the official policy of the Nazi state" and more as "two professors who took advantage of the Nazi state to push their academic agenda, with some early modest success, but eventually the Nazis got sick of them." It made a big splash in the West as an example of how perverse Nazi ideology was, but it's a little more complicated than that.
The biggest "hit" against German science was one of the first laws the Nazis passed after they took power, which fired all non-Aryans from the German civil service. This included all university professors, because of the way the German state was set up. This led to a massive "brain drain" in the years prior to the war, even among scientists who were not Jewish. (Einstein had already left Germany and opted not to return; Planck never left, as an aside.)
In some areas, like physics, Germany went from one of the big three top-tier global scientific powers (along with the UK and France) to a second-tier scientific power (and the "brain drain" of fascism in Europe led to the elevation of the United States to a top-tier power, as an aside).
The Nazis did invest heavily in certain areas of research and development for war. The rocket program is the premier example of this, and their greatest success. The German Army got very interested in rockets during Weimar (because they were not prohibited by the Versailles Treaty), but the Nazis in particular were very taken with the idea of rockets, because they believed they would have massive propaganda value, and because they had fantasies about going into outer space. They gave von Braun's program almost unlimited resources (including slave labor) to accomplish his engineering feats. It is worth noting that as a military investment it was a total failure: the rockets played absolutely no positive role in their war fighting, because they were too crude to be used as anything but terror weapons (and their effect on morale was minimal, maybe even counterproductive). They consumed massive resources that could have been spent better. So while they were technically very impressive, and the US and Soviets made good use of that technology (and the people) in the postwar, they were actually very poor strategic choices.
As with many things, the "Nazis were good at science/technology" is a hit and miss kind of thing. The Germans were top-tier scientists and engineers prior to the Nazis. Some of that could be translated into success under the Nazis, some of it could not. The Nazi state itself was not particularly pro- or anti-science as a rule, but they were willing to spend huge sums on projects they thought had technological applications that were useful to their aims.
For further reading on the Deutsche Physik episode and "brain drain", see Mark Walker, Nazi Science. On the Nazi approach to technology, see Jeffrey Herf, Reactionary Modernism.