I don't know that chaotic is an accurate description for the Nazi governmental structure. Actually, it was quite carefully structured so that 1) it could function efficiently, and 2) so that it could not create power threats to Hitler's rule. It's quite stunning, really, the amount of war materiel Germany manufactured during the war years, especially given the constant allied bombing that disrupted supply lines and population centers, and her limited access to resources later in the war.
The other thing with the chaotic nature of the Nazi government was that they were not allowed to think on their own feet. Everything had to be approved by Hitler, who was not always readily available to give his opinion. He was a supreme micro-manager, and therefore, his plans fell when things got hairy. This is largely why the US military is so successful...their training includes what to do in certain situations and the commander on site is to make those decisions rather than trying to ring the president for every single move.
Actually, this was one of their main problems, and it simply complicated all the rest. Germany did not have the manpower, industrial capacity and access to raw materials to really put the country on what could be termed a proper war footing in the economic sense. The blitzkrieg was designed to compensate by brief flurries of war material (and materiel) production, which would allow the military to stockpile what was needed for the next major campaign, and then switch industry back to consumer goods to keep the economy afloat. Obviously this would only work for short campaigns, which was fine until the invasion of the Soviet Union. The Soviets would have outlasted Germany eventually anyway, even with time gaps between Russian offensives. But those enormous attacks, combined with the steady pressure of campaigns in Africa and the constant low level warfare in occupied territories and oceanic blockade (both traditional British strategies), drained their economy beyond it's long term capacity.
In addition the Germans had seven branches of the military, including the Abwehr and the Todt Organization, each of which had its own factories, distribution corps, research and development, seperate accounting and pay systems, etc. It was too inefficient to stand up to a long war. Additionally, plans for new weapons designs were chaotic, and constantly changing, which caused immense wastage. One example is the jet plane; first a fighter, then a bomber, then a fighter-bomber, each change wasted design and production time, and they ended up with a compromise aircraft which did neither task well. The decision to pursue the jet plane instead of antiaircraft rockets meant that vast resources were wasted on a doomed project while a relatively inexpensive and useful weapon which was more badly needed was ignored. Every aspect of war production fell prey to these problems.
Hitler's method of playing off one group against another (and one person against another) compounded this problem greatly. Aside from Albert Speer and Werner von Braun, most of the people put in charge of programs were not the brightest or most competent available, and were personalities easily dominated by Hitler.
All of these things were made worse by the fact that Germany was not really a large enough country with enough resources to handle the scale and time length of the war. They lost 3,000 tanks in the second battle of Kursk, more than they ever had on the Western Front. Transport of supplies was done mostly by horse drawn wagons throughout the war, because they had no way of manufacturing enough trucks. Troops for the most part moved on foot. Germany simply did not have the economic resources or manpower to win, and they wasted unbelievable amounts of what they had on the ethnic cleansing programs. Terror bombing and the rocket bombs did not achieve any real advance in the war, and wasted more materials and manpower. Chaos was really the thing Hitler appeared to be best at.
The very nature of the government was its own worst enemy. The entire structure and efficiency was built on the whims of Hitler, and he personally involved himself at all levels, regardless of the outcomes. His political machinery operations probably prevented Germany itself from building what it needed to defeat the allies, and his continued focus on non-military matters affected the efficacy of the entire Third Reich. If it wasn't for his own personal biases, prejudices, hatred for others, ect., Germany could have focused on military objectives rather than civilian ones and have won the War.