The upside is it's very easy to see when people are talking about something else, the downside is there's not much else to be said about it that's likely to be fruitful.
Which is of course the whole problem really. Exercises and tests as I mentioned above are only a way to illustrate and transmit theory. You actually have to be standing there with someone to be able to help them do it in my experience.
As to the moving all at once. That is what Tohei talks about when he says 'keep one point'. The hara or one-point is the centre of all movement, all movement should be initiated from here. It is our centre of gravity physically so this makes sense. The problem with being told to 'keep one-point' is that people often become internally focused (no pun intended), they have no awareness of their surroundings and so it is easy to take their mind away from their centre (i.e. by grabbing them elsewhere such as their wrist for example). I often try to help people through this by telling them that they need to look at the horizon. By which I mean, if you are on board a ship and it is bad weather, you get seasick when you look at the rail and you tend to fall down more. If however, you keep your eye focused on the horizon your balance improves and you feel less sick. Same sorta thing needs to happen when you keep one-point.
Also, it's easy to move from your centre but leave other parts of your body behind if they aren't coordinated with your centre. But that's a different story.