The rest of the problem: navigation, motion planning, etc. hasn't changed that much, but is definitely possible on an amateur budget.

The problem with a list of "open problems in robotics" is that just about everything people have come up with has been demonstrated in a lab somewhere. Walking, grasping, manipulation, navigation, swarming, etc. But nobody has managed to combine all those capabilities in a single robot. So the remaining open problem is to solve all the individual problems with one piece of hardware and software.

In terms of navigation, magnetic line following is trivial and more complex navigation really isn't that hard these days. Just look at how any of the modern robovacs navigate.

If you want to generally see where things are I'd recommend checking out some papers or even some writeups from the last icra.

EDIT: Just looked at the Amazon picking challenge for the first time in quite a while and it's not as impressive as I remember it to be.

There have been some great advancements in grasping and embodied decision making lately though, so it could fall soon.