There should be something like an X prize for a recycling device. Take a trash pile, sort through it and get things ready for recycling. This would solve a big environmental and would deliver progress in robotics, vision and AI. I'd be more excited about this than self driving cars.

Perhaps continuous learning. A machine learning system that can adjust to changes over time by retraining itself.

However, training is computationally expensive and generating labels for training data is still done mostly manually by humans. Just like people, a continuous learning algorithm will have trouble distinguishing true from fake and could be corrupted by feeding it fake data. There is machine learning that doesn't require labels, but much of the recent success has been built using human labeled data sets. Human biases get into the labeling, and appear even in the methods of selecting and collecting what data to train on. One way to design continuous learning systems involves wrapping simpler machine learning algorithms with data collection and feedback loops to handle the retraining. Ensuring accuracy is a difficult problem unless your problem domain comes with some built-in measures. Some measures of "correctness" are arbitrary such as those defined by culture and can change over time or geographically.

That's a very good question.

Robot manipulation in unstructured situations is still not very good. (See the videos of the DARPA humanoid challenge) "Common sense", defined as the ability to predict the consequences of actions and to use that to plan, hasn't progressed much in years. Machine learning doesn't seem to have helped much with either, so far. Those are key areas for doing physical things in the real world. Humans are good at those.

So that's where to look for hard problems.

The payoff is low, though. Those skills are common to all healthy humans, so there's a huge pool of unskilled labor available with them. If you did a startup, and you solved, say, robotic shelf stocking, it would not be a huge win over low-wage people.