I'm cooking two dishes that need to cook at different temperatures in the oven, what do I do?
Neither broccoli nor corn is going to be all that picky regarding oven temperature, you'll be fine just splitting the difference. Since corn is the less picky of the two items, I'd go 400F. Expect the broccoli to take slightly longer than the recipe, and the corn to take less time. But don't make yourself nuts about it. Neither corn slightly more done than the recipe expects nor broccoli slightly underdone is going to ruin your meal. Don't overcook your broccoli though! BLECH!