For the bo - we happen to have the larger bo with the very rounded tip. We have only one of the traditional tapered bo - when we use that one I tell people to place the end on their belt knot. But yes - there is some risk there - especially if the training turns too competitive.
Perhaps a better question would be "how do you know when a student is moving from their center?"
...in and out of cat stance
...in and out of kiba dachi
...for a wauke
...for a strike or kick
...for a sweep, lock(break), throw, or take-down
...in yakosuko bunkai
...in oyo bunaki
...in yakosuko kumite
...in jiyu kumite
It is absolutely more than just good posture and it is not moving like Frankenstein.
One of the early trainings that I think helps is when students do the partner wauke exercise with each other - first in a stationary stance and then with sliding or stepping. However if two new students do this together it turns into a wacky kind of arm wrestling. So when possible I try to pair newer students with more experienced students.
I think sometimes we give lip service to "moving from your hara/center" without focusing on what that means in places other than sanchin stepping.
Occasionally, I will also hold a kicking bag or other target in front of the person doing the stepping so they can move from the center against resistance and also try and hit or kick something.
That's a good one.
For the upper level kata movements - I find some moves more difficult than others to do from the center including:
-shoken scooping movement & toss/strike
When Jim Maloney did his Sanseiryu at camp a few years back he showed dynamic and explosive movement in this technique. What he did captures of the feeling of what I'd like to be able to do without taking both feet off the ground. I just don't have enough mass to risk lifting up the way he can. I need the support of the ground to help me bear the body weight at the moment when you beak the balance.
-the step backwards after the kakushiken and leg raise.
The version shown by some is do just step back, steop - and then do the leg raise. Some just step back. Still others move continuously through to the end of the form, stepping back, raising the leg, and stepping into neutral.
For this one the timing has quite a bit to do with what you're doing at the time - however no matter what I'm doing in my head I find this sequence to be particularly challenging.
One of the best ways I found for me to show myself where I weakest in moving from my center when I'm training alone is to do my kata mirror image.
Since this is a training I only do every few weeks I can quickly feel where a movement is less rooted.