In a lot of cases they didn't need to supply much innuendo or rumor. Political smear campaigns and fearmongering and making promises isn't just something that automatically wins votes as you well know. They weren't elected just on 'appeal.' That would be minimizing what a threat they were politically. Underestimating them.
After all, they weren't the first political party in Germany at that time to engage in appealing to the masses.
The Nazis took advantage of the fact that there were too many parties that over the past fifteen years had been engaging in extensive politicking, coalition building, horse trading and other dealings. Between 1923-29 the German people, quite rightly, took heart in that they had overcome Versailles largely and what they felt was a War they had never actually lost and that the economy was recovering. Life was good. And yes, when the Great Depression hit and put everything into a tailspin, it was hard. But that alone, or even with the explanation of Versailles and anti-semitism isn't enough to state why the Nazi's earned such a massive amount of the votes in June of 1932. Why them and not the Communists or some other party, right wing or otherwise? Germans weren't exceptionally anti-Jewish... even the more liberal French were by and large more anti-semitic then the Germans through the twenties and early thirties.
The Nazis, using a network of workers, veterans groups, womens associations, and various other grassroots organizations, was able to respond on the street to the Great Depression. Nazi Party members rarely held conferences in the best hotels like other political parties. They were the ones feeding workers and veterans, they were the ones who supported strikers with food and groceries from Nazi owned restaurants and pubs and grocers. They never spoke of 'class struggles' like the Communists and Social Democrats and pointed out how the liberal Weimar Republic was rolling back social welfare programs while they were pushing forward with their own private charity. Meanwhile their radical rebelliousness alienated the conservatives, and other right wing parties, and all of the smaller parties who were dedicated to certain narrow issues were obviously overwhelmed by the party that was going to put an end to political horse trading and the anarchy that was the current government. Combined with their own message of law and order, of national respect, of increasing economic productivity, saving the welfare state through social reform, of taking advantage of German ingenuity and industry with advances in science and technology, and yes, a little Versailles vengeance in erasing the national shame they felt in November of 1918.
The Nazi Party was fueled by the vibrant political situation in the Weimar Republic. When over a third of Germans voted for the Nazis in June of 1932, they did so because the Nazis were able to harness all of that energy that a free democracy had managed to establish. They were innovative enough to attract right and left wing voters with their message. You can't just do that by blaming the economy or blaming the Jews or blaming Versailles. The Nazi Party was the only party that really managed to capture the German desire to see a party that would unify the German people, not divide them like the numerous parties did before whether through ethnic groups, or religious groups, or by catering to particular German states (Bavaria, Prussia etc) or by classes. (like the three rural parties or the Communists and Social Democrats or the German Party for the Middle Class) If the Nazis focused solely on the Social Democrats or Marxists or Jews or Conservatives, they would've stalled like everyone else, but they didn't because there was plenty of blame to go around. Keep in mind Germany was only made a country only sixty years earlier. The differences between a Saxon and a Bavarian and a Prussian could almost be as vast as the difference between the Irish and English or a Ukrainian and a Finn. The Nazi Party message overcame that and wasn't just the Nazi Party. It was the German Party. For many Germans, voting Nazi seemed like the most democratic vote they ever had.
When you look at the election results, they took votes from the socialists, the liberals, the conservatives, the middle class parties, the protestant parties, and even the rural/farmers parties. You can't win such broad appeal just by rumor and fear mongering. You need a positive platform of your own that is way better then everyone elses without sounding like the second coming of Jesus, because then it'd be fake.
It's telling that the only other party that had any success (and this was due to blaming the Great Depression and the West for Versailles) was the Communist Party in the July 1932 elections. But the Communists (peacefully anyways) would've likely never been able to seize power in Germany. They were crushed in the Spartacist rebellion and even the Socialists saw them as bitter rivals. Plus unlike almost every other party, they would've never earned the support of German businesses and liberals in the government. Added onto that how the class struggle literally alienates significant swaths of the population, they would perpetually face an uphill battle to ever being as popular as the Nazi Party.