George S. Ledyard
What I tell my students:
1) look at the feet - what is the footwork pattern?
2) look at what the arms are doing?
if you get another repetition:
3) look at what the relative timing is of the feet and hands
Most people at the beginning cannot see the whole, they need to break it down into pieces. I still use this method myself on those rare occasions when I see something that I have never seen before.
At least get the footwork. The footwork moves the body and the handwork comes from the body movement so if you get the footwork you have a good chance of getting the rest, even if the teacher didn't do many repetitions.
I think the way of watching changes as you progress. Just like moving, it takes time to learn.
For a beginner, I would recomend to look at the edges: Feet and palms. Pay attention at first to Uke attack, and then to Nage reaction - and in that reaction, focus on his feet (steps) and hands and the relationship between them.
As a beginner, emulating the hand and feet movements, are the first step for learning a technique. As you progress, you will sowly redirect your attention towards the center, but you should not start this way. Just like we do not learn to move from the center out, but rather start learning how to move our edges (hands \ feet) and use them to move the center, and then reverse the process into correct movement (flowing from the center outwards).
A good teacher will assist you by breaking the technique to easy to learn stages and not only perform the technique as one (the latter is the correct execution, but difficult to learn).