Really simple things that shouldn't be heresy. Stuff that isn't even complicated, stuff you can and even do teach in Econ 101! Like, "if searching for and transitioning to a new job is costly, then employers have monopsony power and minimum wage increases are likely to increase, not decrease, employment."
When one criticizes economics along these lines, academic economists will point to all the research about these subjects. But in The Discourse and in policy advice, very little of this stuff ever makes it in. It isn't even that deviations from Econ 101 are treated as unmentionable, it's that deviations from the first 3 weeks of it are.
The inherent monopsony of labor markets is just one example. Generally what are all these Ph.Ds for if, in practice, the entire world is explained by a supply and demand graph you throw up on the screen on first day of freshman econ?