Hitler made a major 'mistake' in the Battle of Britain - a lucky mistake for Britain as it turned out. He insisted on bombing cities and ok, factories in order to cow the British. Of course it only made them all the more determined to resist. He did this against the advice of his generals who had advised first destroying Britain's airforce as it sat on the ground between refuellings. Had he taken their advice, things could have turned out very differently. Instead he left it practically unhindered in attacking his bombers.
That's the problem of having a megalomaniac at the helm. While he did have a few good military ideas, he often overruled the sensible advice of the Wermacht generals who included some of the most able military commanders of the time. An even bigger mistake was to invade Russia, as someone noted further up, without being prepared for the long haul. He probably expected a quick victory, but Stalin moved arms production out of range to siberia, and Russia could 'afford' to lose massive numbers of men (1 million Russians died at Stalingrad alone) that Britain couldn't even have contemplated losing, and still have plenty more. The German attitude to the Russians was also different: they regarded Slavics as 'inferior people' which may be one reason why they underestimated them. They also dealt very harshly with Russians - massacres in Bylorussia, POWs sent to concentration camps etc., Russians in a sense, had a lot more to lose if they lost. British and US POWs on the other hand received far better treatment.
Germany's weaponry was very advanced and their tactics were also leagues ahead of other Western nations at the outbreak of war. The Versailles Treaty had dismantled Germany's army so Hitler had to rebuild the Wermacht from scratch with new weapons. Germany was one of the first countries to use paratroops and supply them with specialised weapons unless I am mistaken.
As regards the British never giving up and fighting to the bitter end.... I'm not so sure about that. The British had already shown what happens when they caved in to foreign occupation - back in 1066 in Hastings. The Normans were never dislodged. The experience of the Channel Islands which were occupied by the Wermacht from early on in the war, gives some flavour of what an occupied UK might have been like. People may not have wanted the Germans there but there wasn't much they could do about it. There was certainly no fight to the death. The British might have had fighting sprirt but they didn't have to contend with German forces actually occupying their soil as the French did. My guess is that Hitler would have allowed the Windsors (who are of German origin anyway) remain on as a kind of caretaker governemnt, like the Vichy regime in France. The Windsors would probably have capitulated and agreed on the basis that it would be better than direct rule from Berlin. But, who knows?
Perhaps like the Normans, the Germans in Britain might have eventually been assimilated rather than driven out as such. Even in Ireland when British military and bureaucratic occupation was finally ended, many elements of the British regime remained.
Incidentally, one excellents book on the Italian peninsula campaign of 1944 -5 is Alan Whicker's 'Whicker's War' (ISBN 10 0-00 720508-2). It's a very honest and humourous account, I think. It also startled me at times about the politics of war, how US Gen.Max Clark allowed Kesselring's armies to escape and form defensive lines because of his insistence on being the man who captured the highly symbolic Rome.