There were a number of things that the Germans could have done differently that fall into the categories of arrogance though arrogance and boldness were there big asset early on so perhaps they could not overcome some of them.
-Hitler delayed going total war in industry & rationing until after things went bad in russia. Women were not fully introduced into the labor force and german production was slowed because of that.
-Japan and Germany both believed their codes were uncrackable, and the Japanese got thumped at midway and the mastermind of Peral harbor got shot down directly because of it. The cracking of german codes because of presumed infallability, led to tracking & sinking of german subs, troop deployment info etc, giving th allies a serious advantage and likely preventing the british from being more seriously starved out of supplies, food etc,. Had germans understood their codes were not uncrackable and had been directed to change their dials (Those of you familiar with enigma) each time they sent messages or even monthly or weekly then code cracking would have been near impossible.
-Had hitler not apparently punished his generals (per some shows I have seen on the history channel) by first pausing them at the scene of a german surrender for a day or so and then by pulling them back at dunkirk and letting Goerings airforce try to wipe them out then perhaps the germans would have prevented most of the 400,000 or so britsh and french soldiers who escaped from doing so. Those soldiers washed arrived on British soil, were rearmed and potential threats to any future german invasion or at least a morale boost. later those same soldiers were used against the germans from Africa to Italy to the invasion of Europe. Had even half of them been killed or caught think of the negotiating chip for a surrender or armistice with Britain, think of the morale killing effect of losing that many fighting men, think of the more intense draft the British would have had to implement, think of the French agents from that pool that the british could not insert in to france to organize resistance etc etc. Hitler sometimes screwed around due to his arrogance and it cost him.
Things that are not about arrogance that could have made a difference. More hindsight and ideology than arrogance.
- Had Hitler sent some paratroopers to assist the Italians in Greece, not that they knew the Italians would screw that up, then perhaps he would not have had to commit late in the game so many planes and troopers that it would delay his Russian invasion.
- Bigger is not better. Hitler loved big. The king tiger was too big. There was a massive transport glider that was a dangerous waste. He invested in several pocket battle ships despite knowing that the brits had overwhelming naval power. More money and resources into big tank guns and incremental change in proven models would probably have served them better.
-Some think that had he invested the money in giving the navy several dozen to perhaps 100 more submarines before the war started that the blockade against England may have forced them to surrender, and would also have meant far less supplies eventually have got to the Russians.
-In some cities half of the german doctors before Hitler came to power were jewish. The extermination of the Jewish people and their eradication from society likely boosted german casualties somewhat significantly and may have meant that averge daily forces in combat were lowered by one to several percentage points because of this and day by day that matters. ideologically it was probably a non starter to have saved the doctors or have saved their families by giving them new identities and let them serve in combat. The Jewish question rallied the german people, aided hitlers rise and if he had not gone after them he may not have risen to power in the first place in a perverse way, so only a hostage situation with them in field hospitals probably would be the alternative that could have helped but it would not have happened.
-The failure to train more pilots prior to the war. In the end they had planes, too little fuel and too few pilots.