I would recommend e.g. this page for a fair review of the dropping unemployment figures. Before Hitler took over, the Weimar Republic's body of unemployed citizens peaked at 6 million people. The figure was dramatically decreasing down to the figure of only 300,000 people (a decrease by a factor of 20) in 1939.
However, that doesn't mean that this decrease was a universally good thing. It seems fair to say that it was "mostly bad".
- First, let me start with the only aspect I consider "mostly good": lots of new big-government projects were started, new highways, irrigation projects etc. that needed lots of workers (well, many people were proud about it but at the end, I and others just don't think that such a big part of the economy should be driven by the government, even when it comes to building the infrastructure)
- A related point is that the funding of many of these things was from huge budget deficits and the public debt skyrocketed. Various "new forms of the government debt" were spreading. The deficit in 1939 was 38 billion marks – clearly an unsustainable dynamics in normal circumstances. The detachment of these figures from the economic reality made "something big" as the war pretty much necessary by itself. See Economy of Nazi Germany on Wikipedia for some detailed data.
- Second, much of the legitimate reduction of unemployment among the workers was started when the weapons began to be mass-produced for Germany to become a military power, and that increase of the military strength of Germany was a major force that made the war unavoidable later (which is why I count this point as a negative)
- Third, women were completely eliminated from the statistics, so basically a factor-of-two decrease may be considered a bureaucratic trick for this reason (also something showing that the Third Reich was sick; here, where we had the Protectorate of Bohemia and Moravia, all men were obliged to be members of the "National Conviviality" while women were totally eliminated from that, too – I don't think that this perfect segregation of the sexes belongs to a civilized society)
- Jews lost their citizenship in 1935 and were eliminated from the statistics – even though the Jewish unemployment probably grew during Hitler's reign (while their later fate was much worse than just unemployment; a catastrophic point for the picture of the Third Reich)
- Even non-Jewish unemployed citizens were likely to be labeled "work-shy" and moved to the concentration camp so everyone was "encouraged" to work in this brutal way (sorry but that just doesn't happen in civilized countries)
- Conscription took lots of young men off the unemployment tables (5 million German troops paid their life for this move to "reduce the unemployment", a little bit too high a price – the military casualties almost match all the unemployed people during the Weimar peak)
- Much like the USSR and the communist countries later, the Nazi regime was ideologically obsessed with this "virtue" of almost non-existent unemployment. That also answers your other question: Obviously, all the communist bloc countries should be considered analogous – and, as the points above make clear, no decent free democratic country may be considered analogous in those respects. As a kid, I grew up in late communist Czechoslovakia and we were constantly impressed by the idea that there was no unemployment in the Soviet bloc. The reasons were pretty similar. The sane among us never thought that this "non-existent unemployment" was a good enough excuse for virtually all aspects of our nation and its economy to be so brutally damaged.
With one exception, almost all the reasons for the dramatically dropping figures were bad. And economists would generally agree that the super-low unemployment in Germany was a bad outcome, anyway. Companies need some nontrivial pool from which they can hire when someone leaves or dies or a pool that allows them to expand or reshuffle etc. 300,000 people was unquestionably a pathologically low number for a country of Germany's size.
Too bad, there still exist people who are so obsessed with the reduction of the unemployment rate that they could be ready to do similar things that were taking place in Germany of the 1930s. I personally find it totally fine to appreciate things that worked even when we're talking about an unpopular and inhuman country such as the Third Reich (and I think that even on our occupied territory, there were things that just "worked"). But I am convinced that the people who think that the whole "package" leading to the low unemployment in the Third Reich – the reasons, methods, and the results – was a "good thing" are much closer in their reasoning to the Nazi (or otherwise totalitarian) reasoning than they are probably willing to admit.