People often see the politics of appeasement worked up by Britain and France in the build-up to WWII with disgust or irony, perhaps the way they would view two bodybuilders donating machine guns to a skinny starving art major who took up rape as a career. A careful investigation of the socio-cultural, political build-up and the military situation before WWII changes the scenery. The British and French operated in appeasement not out of the naive assumption that Hitler would suddenly be a good boy if they gave him the toys he wanted, but out of a fear and distrust for each other and for the rest of the world.
Yes, Britain and France underestimated Hitler—and Stalin, and Mussolini, and the post-Meiji government in Japan, for that matter. Hitler's rise to power occurred so subversively that putting a finger on him would have proved impossible, especially in a world where both Britain and France had their economies to focus on. He engineered sex scandals to manipulate public opinion and continually went behind the backs of the national community to make territorial demands. Stalin also appeared wildly popular to the people from the outside. Both France and Britain had difficulty becoming aggressive with dictators because they had difficulty seeing their next move.
The underestimation of Hitler had more to do with the situation in France and Britain than with Hitler's cleverness or British and French naivete, however. With France's late economic crash relative to the rest of the Western World, the French people had little time to focus on developing a military in response to Hitler. Pride prevented France from using German tanks and caused her to trust the Magineau line instead--even though some the Magineau's newest military technology had been there for over 25 years. As explained in lecture, France included colonial holdings when counting the military, even though the colonies would not prove terribly useful to France in the actual event of War. Additionally, France had several government overhauls during this period. In Britain, the US had become the main economic enemy so that Britain had little time to spare looking for a madman they didn't believe in. Britain acquiesed to Japanese invasion of China because they wanted Japan to acknowledge their control over India. No one had time for dictators when finances were on the line. Even Hitler's anti-semitism tipped no one off, for anti-semitism had grown much more rampant in Britain and other Western nations than in Germany; indeed, German Jews considered themselves Germans first, Jews second, in many cases, because they had received better treatment in Germany than elsewhere.
Nevertheless, it was not ignorance or complacency so much as fear that prevented France and Britain from behaving firmly towards Germany. Products of the generation that had grown up afraid of war had a strong fear of misjudging Hitler as Germany had been misjudged in WWI: they remembered how the wildly exaggerated propaganda at the beginning of the war had drawn them into so much misery. Not only fear of war, but also fear of each other kept the allies from acting while Germany re-armed. A bug in DeGualle's dining room revealed that he felt the real enemies lay in Britain and the US, and many in Europe felt Roosevelt posed a greater threat than Hitler. During the formation of the Munich Pact, the way that Hitler manipulated the Germans in the Suedentenland to revolt passed completely under the radar because France worried much more about whether or not they would have Britain on their side diplomatically. Britain didn't want to make an alliance with Russia against Germany for fear of angering Japan, Russia's age-old rival. Alliances drawn and re-drawn between cconomic and military rivals left every country afraid of the others, and in a sea of sharks, the one shark with a swastika does not stand out much. Fear, not complacency, had the reigning power in the appeasement.