There definitely needs to be a tutorial on wards and corrier (probably for supports, and lion is probably better than shaman for learning)

Would love a "map awareness" tutorial (short one) just to teach new people how to effectively use the minimap.

There also really needs to be one on item build up since it confuses a lot of new players. Maybe picking a hero who has a items that require a lot of build up?

There should also really be a "last hit challenge" in the learning section, so people can practice last hitting without having to go find the custom game. Or conversely, make them download the last hit challenge as part of the tutorial so they have the resource.

Maybe have a set of "completely new" tutorials (movement, what gold is, dying, corrier control), beginner tutorials (why buying back is bad, importance of early game items, roles in Dota/basic lanes), medium tutorials (higher last hit goal, map awareness + warding, different types of damage, slows vs stuns vs silences vs hexes) and advanced (creep aggro, walk through WHY a couple of sample heroes buy what they buy (needs actual current builds though) control groups/beginning micro)